/* 
A* -------------------------------------------------------------------
B* This file contains source code for the PyMOL computer program
C* Copyright (c) Schrodinger, LLC. 
D* -------------------------------------------------------------------
E* It is unlawful to modify or remove this copyright notice.
F* -------------------------------------------------------------------
G* Please see the accompanying LICENSE file for further information. 
H* -------------------------------------------------------------------
I* Additional authors of this source file include:
-* Jacques Leroy (matrix inversion)
-* Thomas Malik (matrix multiplication)
-* Whoever wrote EISPACK
Z* -------------------------------------------------------------------
*/
#include"os_python.h"
#include"os_predef.h"
#include"os_std.h"

#include"Base.h"
#include"Vector.h"
#include"Matrix.h"
#include"MemoryDebug.h"
#include"Ortho.h"
#include"Feedback.h"
#include"Setting.h"


/* Jenarix owned types, aliases, and defines */

#define xx_os_malloc mmalloc
#define xx_os_free mfree
#define xx_os_memcpy memcpy
#define xx_os_memset memset
#define xx_fabs fabs
#define xx_sqrt sqrt
#define xx_sizeof sizeof
#define xx_float64 double
#define xx_word int
#define xx_boolean int

#ifndef XX_TRUE
#define XX_TRUE 1
#endif
#ifndef XX_FALSE
#define XX_FALSE 0
#endif
#ifndef XX_NULL
#define XX_NULL NULL
#endif

#define XX_MATRIX_STACK_STORAGE_MAX 5


/* 
   for column-major(Fortran/OpenGL) use: (col*size + row)
   for row-major(C) use: (row*size + col)
*/

#define XX_MAT(skip,row,col) (((row)*(skip)) + col)

xx_boolean xx_matrix_jacobi_solve(xx_float64 * e_vec, xx_float64 * e_val,
                                  xx_word * n_rot, xx_float64 * input, xx_word size)


/* eigenvalues and eigenvectors for a real symmetric matrix 
   NOTE: transpose the eigenvector matrix to get eigenvectors */
{
  xx_float64 stack_A_tmp[XX_MATRIX_STACK_STORAGE_MAX * XX_MATRIX_STACK_STORAGE_MAX];
  xx_float64 stack_b_tmp[XX_MATRIX_STACK_STORAGE_MAX];
  xx_float64 stack_z_tmp[XX_MATRIX_STACK_STORAGE_MAX];
  xx_float64 *A_tmp = XX_NULL;
  xx_float64 *b_tmp = XX_NULL;
  xx_float64 *z_tmp = XX_NULL;
  xx_boolean ok = XX_TRUE;

  if(size > XX_MATRIX_STACK_STORAGE_MAX) {
    A_tmp = (xx_float64 *) xx_os_malloc(xx_sizeof(xx_float64) * size * size);
    b_tmp = (xx_float64 *) xx_os_malloc(xx_sizeof(xx_float64) * size);
    z_tmp = (xx_float64 *) xx_os_malloc(xx_sizeof(xx_float64) * size);
    if(!(A_tmp && b_tmp && z_tmp))
      ok = XX_FALSE;
  } else {
    A_tmp = stack_A_tmp;
    b_tmp = stack_b_tmp;
    z_tmp = stack_z_tmp;
  }

  if(ok) {

    xx_os_memset(e_vec, 0, xx_sizeof(xx_float64) * size * size);
    xx_os_memcpy(A_tmp, input, xx_sizeof(xx_float64) * size * size);

    {
      xx_word p;
      for(p = 0; p < size; p++) {
        e_vec[XX_MAT(size, p, p)] = 1.0;
        e_val[p] = b_tmp[p] = A_tmp[XX_MAT(size, p, p)];
        z_tmp[p] = 0.0;
      }
      *n_rot = 0;
    }
    {
      xx_word i;
      for(i = 0; i < 50; i++) {
        xx_float64 thresh;

        {
          xx_word p, q;
          xx_float64 sm = 0.0;
          for(p = 0; p < (size - 1); p++) {
            for(q = p + 1; q < size; q++) {
              sm += xx_fabs(A_tmp[XX_MAT(size, p, q)]);
            }
          }
          if(sm == 0.0)
            break;
          if(i < 3) {
            thresh = 0.2 * sm / (size * size);
          } else {
            thresh = 0.0;
          }
        }

        {
          xx_word p, q;
          xx_float64 g;

          for(p = 0; p < (size - 1); p++) {
            for(q = p + 1; q < size; q++) {
              g = 100.0 * xx_fabs(A_tmp[XX_MAT(size, p, q)]);
              if((i > 3) &&
                 ((xx_fabs(e_val[p]) + g) == xx_fabs(e_val[p])) &&
                 ((xx_fabs(e_val[q]) + g) == xx_fabs(e_val[q]))) {
                A_tmp[XX_MAT(size, p, q)] = 0.0;
              } else if(xx_fabs(A_tmp[XX_MAT(size, p, q)]) > thresh) {
                xx_float64 t;
                xx_float64 h = e_val[q] - e_val[p];
                if((xx_fabs(h) + g) == xx_fabs(h)) {
                  t = A_tmp[XX_MAT(size, p, q)] / h;
                } else {
                  xx_float64 theta = 0.5 * h / A_tmp[XX_MAT(size, p, q)];
                  t = 1.0 / (xx_fabs(theta) + xx_sqrt(1.0 + theta * theta));
                  if(theta < 0.0)
                    t = -t;
                }
                {
                  xx_float64 c = 1.0 / xx_sqrt(1.0 + t * t);
                  xx_float64 s = t * c;
                  xx_float64 tau = s / (1.0 + c);

                  h = t * A_tmp[XX_MAT(size, p, q)];
                  z_tmp[p] -= h;
                  z_tmp[q] += h;
                  e_val[p] -= h;
                  e_val[q] += h;
                  A_tmp[XX_MAT(size, p, q)] = 0.0;
                  {
                    xx_word j;
                    for(j = 0; j < p; j++) {
                      g = A_tmp[XX_MAT(size, j, p)];
                      h = A_tmp[XX_MAT(size, j, q)];
                      A_tmp[XX_MAT(size, j, p)] = g - s * (h + g * tau);
                      A_tmp[XX_MAT(size, j, q)] = h + s * (g - h * tau);
                    }
                    for(j = p + 1; j < q; j++) {
                      g = A_tmp[XX_MAT(size, p, j)];
                      h = A_tmp[XX_MAT(size, j, q)];
                      A_tmp[XX_MAT(size, p, j)] = g - s * (h + g * tau);
                      A_tmp[XX_MAT(size, j, q)] = h + s * (g - h * tau);
                    }
                    for(j = q + 1; j < size; j++) {
                      g = A_tmp[XX_MAT(size, p, j)];
                      h = A_tmp[XX_MAT(size, q, j)];
                      A_tmp[XX_MAT(size, p, j)] = g - s * (h + g * tau);
                      A_tmp[XX_MAT(size, q, j)] = h + s * (g - h * tau);
                    }
                    for(j = 0; j < size; j++) {
                      g = e_vec[XX_MAT(size, j, p)];
                      h = e_vec[XX_MAT(size, j, q)];
                      e_vec[XX_MAT(size, j, p)] = g - s * (h + g * tau);
                      e_vec[XX_MAT(size, j, q)] = h + s * (g - h * tau);
                    }
                  }
                  (*n_rot)++;
                }
              }
            }
          }
          for(p = 0; p < size; p++) {
            b_tmp[p] += z_tmp[p];
            e_val[p] = b_tmp[p];
            z_tmp[p] = 0.0;
          }
        }
      }
    }
  }
  if(A_tmp && (A_tmp != stack_A_tmp))
    xx_os_free(A_tmp);
  if(b_tmp && (b_tmp != stack_b_tmp))
    xx_os_free(b_tmp);
  if(z_tmp && (z_tmp != stack_z_tmp))
    xx_os_free(z_tmp);
  return ok;
}

static xx_word xx_matrix_decompose(xx_float64 * matrix, xx_word size,
                                   xx_word * permute, xx_word * parity)
{

  xx_boolean ok = XX_TRUE;
  xx_float64 stack_storage[XX_MATRIX_STACK_STORAGE_MAX];
  xx_float64 *storage = XX_NULL;

  if(size > XX_MATRIX_STACK_STORAGE_MAX) {
    storage = (xx_float64 *) xx_os_malloc(xx_sizeof(xx_float64) * size);
    if(!storage)
      ok = false;
  } else {
    storage = stack_storage;
  }

  *parity = 1;

  if(ok) {
    xx_word i, j;
    for(i = 0; i < size; i++) {
      xx_float64 max_abs_value = 0.0;
      for(j = 0; j < size; j++) {
        xx_float64 test_abs_value = xx_fabs(matrix[XX_MAT(size, i, j)]);
        if(max_abs_value < test_abs_value)
          max_abs_value = test_abs_value;
      }
      if(max_abs_value == 0.0) {
        ok = XX_FALSE;          /* singular matrix -- no inverse */
        break;
      }
      storage[i] = 1.0 / max_abs_value;
    }
  }
  if(ok) {
    xx_word i, j, k, i_max = 0;

    for(j = 0; j < size; j++) {

      for(i = 0; i < j; i++) {
        xx_float64 sum = matrix[XX_MAT(size, i, j)];
        for(k = 0; k < i; k++) {
          sum = sum - matrix[XX_MAT(size, i, k)] * matrix[XX_MAT(size, k, j)];
        }
        matrix[XX_MAT(size, i, j)] = sum;
      }

      {
        xx_float64 max_product = 0.0;
        for(i = j; i < size; i++) {
          xx_float64 sum = matrix[XX_MAT(size, i, j)];
          for(k = 0; k < j; k++) {
            sum = sum - matrix[XX_MAT(size, i, k)] * matrix[XX_MAT(size, k, j)];
          }
          matrix[XX_MAT(size, i, j)] = sum;
          {
            xx_float64 test_product = storage[i] * xx_fabs(sum);
            if(max_product <= test_product) {
              max_product = test_product;
              i_max = i;
            }
          }
        }
      }

      if(j != i_max) {
        for(k = 0; k < size; k++) {
          xx_float64 tmp = matrix[XX_MAT(size, i_max, k)];
          matrix[XX_MAT(size, i_max, k)] = matrix[XX_MAT(size, j, k)];
          matrix[XX_MAT(size, j, k)] = tmp;
        }
        *parity = (0 - *parity);
        storage[i_max] = storage[j];
      }

      permute[j] = i_max;
      if(matrix[XX_MAT(size, j, j)] == 0.0) {
        /* here we have a choice: */
        /* or (B): fail outright */
        ok = false;
        break;
      }

      if(j != (size - 1)) {
        xx_float64 tmp = 1.0 / matrix[XX_MAT(size, j, j)];
        for(i = j + 1; i < size; i++) {
          matrix[XX_MAT(size, i, j)] *= tmp;
        }
      }
    }
  }
  if(storage && (storage != stack_storage))
    xx_os_free(storage);
  return ok;
}

static void xx_matrix_back_substitute(xx_float64 * result, xx_float64 * decomp,
                                      xx_word size, xx_word * permute)
{
  {
    xx_word i, ii;
    ii = -1;
    for(i = 0; i < size; i++) {
      xx_word p = permute[i];
      xx_float64 sum = result[p];
      result[p] = result[i];
      if(ii >= 0) {
        xx_word j;
        for(j = ii; j < i; j++) {
          sum = sum - decomp[XX_MAT(size, i, j)] * result[j];
        }
      } else if(sum != 0.0) {
        ii = i;
      }
      result[i] = sum;
    }
  }

  {
    xx_word i, j;
    for(i = size - 1; i >= 0; i--) {
      xx_float64 sum = result[i];
      for(j = i + 1; j < size; j++) {
        sum = sum - decomp[XX_MAT(size, i, j)] * result[j];
      }
      result[i] = sum / decomp[XX_MAT(size, i, i)];
    }
  }
}

xx_boolean xx_matrix_invert(xx_float64 * result, xx_float64 * input, xx_word size)
{
  xx_float64 stack_mat_tmp[XX_MATRIX_STACK_STORAGE_MAX * XX_MATRIX_STACK_STORAGE_MAX];
  xx_float64 stack_dbl_tmp[XX_MATRIX_STACK_STORAGE_MAX];
  xx_word stack_int_tmp[XX_MATRIX_STACK_STORAGE_MAX];
  xx_float64 *mat_tmp = XX_NULL;
  xx_float64 *dbl_tmp = XX_NULL;
  xx_word *int_tmp = XX_NULL;
  xx_word parity = 0;
  xx_word ok = XX_TRUE;

  if(size > XX_MATRIX_STACK_STORAGE_MAX) {
    mat_tmp = (xx_float64 *) xx_os_malloc(xx_sizeof(xx_float64) * size * size);
    dbl_tmp = (xx_float64 *) xx_os_malloc(xx_sizeof(xx_float64) * size);
    int_tmp = (xx_word *) xx_os_malloc(xx_sizeof(xx_word) * size);
    if(!(mat_tmp && dbl_tmp && int_tmp))
      ok = XX_FALSE;
  } else {
    mat_tmp = stack_mat_tmp;
    dbl_tmp = stack_dbl_tmp;
    int_tmp = stack_int_tmp;
  }

  if(ok) {
    ok = XX_FALSE;
    memcpy(mat_tmp, input, xx_sizeof(xx_float64) * size * size);

    if(xx_matrix_decompose(mat_tmp, size, int_tmp, &parity)) {
      xx_word i, j;
      for(j = 0; j < size; j++) {
        memset(dbl_tmp, 0, xx_sizeof(xx_float64) * size);
        dbl_tmp[j] = 1.0;
        xx_matrix_back_substitute(dbl_tmp, mat_tmp, size, int_tmp);
        for(i = 0; i < size; i++) {
          result[XX_MAT(size, i, j)] = dbl_tmp[i];
        }
      }
      ok = XX_TRUE;
    }
  }
  /* clean up */
  if(mat_tmp && (mat_tmp != stack_mat_tmp))
    xx_os_free(mat_tmp);
  if(dbl_tmp && (dbl_tmp != stack_dbl_tmp))
    xx_os_free(dbl_tmp);
  if(int_tmp && (int_tmp != stack_int_tmp))
    xx_os_free(int_tmp);
  return ok;
}

#undef XX_MAT

int MatrixInvTransformExtentsR44d3f(double *matrix,
                                    float *old_min, float *old_max,
                                    float *new_min, float *new_max)
{
  /* just brute-forcing this for now... */
  int a;
  int c;

  double inp_min[3], inp_max[3];
  double out_min[3], out_max[3];
  double inp_tst[3], out_tst[3];

  if(!matrix)
    return 0;

  copy3f3d(old_min, inp_min);
  copy3f3d(old_max, inp_max);

  for(c = 0; c < 8; c++) {
    inp_tst[0] = c & 0x1 ? inp_min[0] : inp_max[0];
    inp_tst[1] = c & 0x2 ? inp_min[1] : inp_max[1];
    inp_tst[2] = c & 0x4 ? inp_min[2] : inp_max[2];

    inverse_transform44d3d(matrix, inp_tst, out_tst);
    if(!c) {
      copy3d(out_tst, out_max);
      copy3d(out_tst, out_min);
    } else {
      for(a = 0; a < 3; a++) {
        if(out_min[a] > out_tst[a])
          out_min[a] = out_tst[a];
        if(out_max[a] < out_tst[a])
          out_max[a] = out_tst[a];
      }
    }
  }
  copy3d3f(out_min, new_min);
  copy3d3f(out_max, new_max);
  return 1;
}

int MatrixTransformExtentsR44d3f(double *matrix,
                                 float *old_min, float *old_max,
                                 float *new_min, float *new_max)
{
  /* just brute-forcing this for now... */
  int a;
  int c;

  double inp_min[3], inp_max[3];
  double out_min[3], out_max[3];
  double inp_tst[3], out_tst[3];

  if(!matrix)
    return 0;

  copy3f3d(old_min, inp_min);
  copy3f3d(old_max, inp_max);

  for(c = 0; c < 8; c++) {
    inp_tst[0] = c & 0x1 ? inp_min[0] : inp_max[0];
    inp_tst[1] = c & 0x2 ? inp_min[1] : inp_max[1];
    inp_tst[2] = c & 0x4 ? inp_min[2] : inp_max[2];

    transform44d3d(matrix, inp_tst, out_tst);
    if(!c) {
      copy3d(out_tst, out_max);
      copy3d(out_tst, out_min);
    } else {
      for(a = 0; a < 3; a++) {
        if(out_min[a] > out_tst[a])
          out_min[a] = out_tst[a];
        if(out_max[a] < out_tst[a])
          out_max[a] = out_tst[a];
      }
    }
  }
  copy3d3f(out_min, new_min);
  copy3d3f(out_max, new_max);
  return 1;
}

/*========================================================================*/
int *MatrixFilter(float cutoff, int window, int n_pass, int nv, float *v1, float *v2)
{
  int *flag;
  float center1[3], center2[3];
  int a, b, c, cc;
  float *vv1, *vv2;
  float *dev, avg_dev;
  int wc;
  int start, finish;
  int cnt;

  flag = Alloc(int, nv);        /* allocate flag matrix */
  dev = Alloc(float, nv);       /* allocate matrix for storing deviations */

  for(a = 0; a < nv; a++) {
    flag[a] = true;
  }
  for(c = 0; c < n_pass; c++) {

    /* find the geometric center */

    cc = 0;
    copy3f(v1, center1);
    copy3f(v2, center2);
    for(a = 1; a < nv; a++) {
      if(flag[a]) {
        add3f(v1, center1, center1);
        add3f(v2, center2, center2);
        cc++;
      }
    }
    if(cc) {
      scale3f(center1, 1.0F / cc, center1);
      scale3f(center2, 1.0F / cc, center2);
    }

    /* store average deviation from it */
    avg_dev = 0.0F;
    cc = 0;
    for(a = 0; a < nv; a++) {
      if(flag[a]) {
        vv1 = v1 + 3 * a;
        vv2 = v2 + 3 * a;
        dev[a] = (float) fabs(diff3f(center1, vv1) - diff3f(center2, vv2));
        avg_dev += dev[a];
        cc++;
      }
    }
    if(cc) {
      avg_dev /= cc;

      if(avg_dev > R_SMALL4) {

        /* eliminate pairs that are greater than cutoff */

        for(a = 0; a < nv; a++) {
          if((dev[a] / avg_dev) > cutoff)
            flag[a] = false;
          dev[a] = 0.0F;
        }

        /* the grossest outliers have been eliminated -- now for the more subtle ones... */

        /* run a sliding window along the sequence, measuring how deviations of a particular atom compare
         * to the surrounding atoms.   Then eliminate the outliers. */

        for(a = 0; a < nv; a++) {
          if(flag[a]) {

            /* define a window of active pairs surrounding this residue */

            cnt = window;
            b = a;
            start = a;
            finish = a;
            while(cnt > (window / 2)) { /* back up to half window size */
              if(b < 0)
                break;
              if(flag[b]) {
                start = b;
                cnt--;
              }
              b--;
            }
            b = a + 1;
            while(cnt > 0) {    /* go forward to complete window */
              if(b >= nv)
                break;
              if(flag[b]) {
                finish = b;
                cnt--;
              }
              b++;
            }
            b = start - 1;
            while(cnt > 0) {    /* back up more if necc. */
              if(b < 0)
                break;
              if(flag[b]) {
                start = b;
                cnt--;
              }
              b--;
            }

            if((finish - start) >= window) {

              /* compute geometric center of the window */

              wc = 0;
              for(b = start; b <= finish; b++)
                if(flag[b]) {
                  vv1 = v1 + 3 * b;
                  vv2 = v2 + 3 * b;
                  if(!wc) {
                    copy3f(vv1, center1);
                    copy3f(vv2, center2);
                  } else {
                    add3f(v1, center1, center1);
                    add3f(v2, center2, center2);
                  }
                  wc++;
                }
              if(wc) {
                scale3f(center1, 1.0F / wc, center1);
                scale3f(center2, 1.0F / wc, center2);

                /* compute average deviation over window */
                avg_dev = 0.0F;
                wc = 0;
                for(b = start; b <= finish; b++)
                  if(flag[b]) {
                    vv1 = v1 + 3 * b;
                    vv2 = v2 + 3 * b;
                    avg_dev += (float) fabs(diff3f(center1, vv1) - diff3f(center2, vv2));
                    wc++;
                  }
                if(wc) {        /* store ratio of the actual vs. average deviation */
                  avg_dev /= wc;
                  vv1 = v1 + 3 * a;
                  vv2 = v2 + 3 * a;
                  if(avg_dev > R_SMALL4)
                    dev[a] =
                      (float) fabs(diff3f(center1, vv1) - diff3f(center2, vv2)) / avg_dev;
                  else
                    dev[a] = 0.0F;
                }
              }
            }
          }
        }
        /* now eliminate those above cutoff */
        for(a = 0; a < nv; a++)
          if(flag[a])
            if(dev[a] > cutoff)
              flag[a] = false;
      }
    }
  }
  FreeP(dev);
  return flag;
}


/*========================================================================*/
void MatrixTransformTTTfN3f(unsigned int n, float *q, float *m, float *p)
{
  register const float m0 = m[0], m4 = m[4], m8 = m[8], m12 = m[12];
  register const float m1 = m[1], m5 = m[5], m9 = m[9], m13 = m[13];
  register const float m2 = m[2], m6 = m[6], m10 = m[10], m14 = m[14];
  register const float m3 = m[3], m7 = m[7], m11 = m[11];
  register float p0, p1, p2;
  while(n--) {
    p0 = *(p++) + m12;
    p1 = *(p++) + m13;
    p2 = *(p++) + m14;
    *(q++) = m0 * p0 + m1 * p1 + m2 * p2 + m3;
    *(q++) = m4 * p0 + m5 * p1 + m6 * p2 + m7;
    *(q++) = m8 * p0 + m9 * p1 + m10 * p2 + m11;
  }
}


/*========================================================================*/
void MatrixTransformR44fN3f(unsigned int n, float *q, float *m, float *p)
{
  register const float m0 = m[0], m4 = m[4], m8 = m[8];
  register const float m1 = m[1], m5 = m[5], m9 = m[9];
  register const float m2 = m[2], m6 = m[6], m10 = m[10];
  register const float m3 = m[3], m7 = m[7], m11 = m[11];
  register float p0, p1, p2;
  while(n--) {
    p0 = *(p++);
    p1 = *(p++);
    p2 = *(p++);
    *(q++) = m0 * p0 + m1 * p1 + m2 * p2 + m3;
    *(q++) = m4 * p0 + m5 * p1 + m6 * p2 + m7;
    *(q++) = m8 * p0 + m9 * p1 + m10 * p2 + m11;
  }
}


/*========================================================================*/
void MatrixGetRotationC44f(float *m44, const float angle,
                           const float x, const float y, const float z)
{
  float m33[9];
  rotation_matrix3f(angle, x, y, z, m33);
  m44[0] = m33[0];
  m44[1] = m33[3];
  m44[2] = m33[6];
  m44[3] = 0.0F;
  m44[4] = m33[1];
  m44[5] = m33[4];
  m44[6] = m33[7];
  m44[7] = 0.0F;
  m44[8] = m33[2];
  m44[9] = m33[5];
  m44[10] = m33[8];
  m44[11] = 0.0F;
  m44[12] = 0.0F;
  m44[13] = 0.0F;
  m44[14] = 0.0F;
  m44[15] = 1.0F;
}


/*========================================================================*/
void MatrixRotateC44f(float *m, const float angle, const float x, const float y,
                      const float z)
{
  float m33[9];
  float m44[16];
  rotation_matrix3f(angle, x, y, z, m33);
  m44[0] = m33[0];
  m44[1] = m33[1];
  m44[2] = m33[2];
  m44[3] = 0.0F;
  m44[4] = m33[3];
  m44[5] = m33[4];
  m44[6] = m33[5];
  m44[7] = 0.0F;
  m44[8] = m33[6];
  m44[9] = m33[7];
  m44[10] = m33[8];
  m44[11] = 0.0F;
  m44[12] = 0.0F;
  m44[13] = 0.0F;
  m44[14] = 0.0F;
  m44[15] = 1.0F;
  MatrixMultiplyC44f(m44, m);
}


/*========================================================================*/
void MatrixTranslateC44f(float *m, const float x, const float y, const float z)
{
  m[12] = m[0] * x + m[4] * y + m[8] * z + m[12];
  m[13] = m[1] * x + m[5] * y + m[9] * z + m[13];
  m[14] = m[2] * x + m[6] * y + m[10] * z + m[14];
  m[15] = m[3] * x + m[7] * y + m[11] * z + m[15];
}


/*========================================================================*/
void MatrixMultiplyC44f(const float *b, float *m)
{
  /* This routine included in PyMOL under the terms of the 
   * MIT consortium license for Brian Paul's Mesa, from which it was derived. */
  /* original author: Thomas Malik */

  int i;

#define A(row,col)  m[(col<<2)+row]
#define B(row,col)  b[(col<<2)+row]
#define P(row,col)  m[(col<<2)+row]

  /* i-te Zeile */
  for(i = 0; i < 4; i++) {
    float ai0 = A(i, 0), ai1 = A(i, 1), ai2 = A(i, 2), ai3 = A(i, 3);
    P(i, 0) = ai0 * B(0, 0) + ai1 * B(1, 0) + ai2 * B(2, 0) + ai3 * B(3, 0);
    P(i, 1) = ai0 * B(0, 1) + ai1 * B(1, 1) + ai2 * B(2, 1) + ai3 * B(3, 1);
    P(i, 2) = ai0 * B(0, 2) + ai1 * B(1, 2) + ai2 * B(2, 2) + ai3 * B(3, 2);
    P(i, 3) = ai0 * B(0, 3) + ai1 * B(1, 3) + ai2 * B(2, 3) + ai3 * B(3, 3);
  }

#undef A
#undef B
#undef P
}


/*========================================================================*/
void MatrixTransformC44f3f(float *m, float *q, float *p)
{
  register float q0 = *q, q1 = *(q + 1), q2 = *(q + 2);
  p[0] = m[0] * q0 + m[4] * q1 + m[8] * q2 + m[12];
  p[1] = m[1] * q0 + m[5] * q1 + m[9] * q2 + m[13];
  p[2] = m[2] * q0 + m[6] * q1 + m[10] * q2 + m[14];
}


/*========================================================================*/
void MatrixTransformC44f4f(float *m, float *q, float *p)
{
  register float q0 = *q, q1 = *(q + 1), q2 = *(q + 2);
  p[0] = m[0] * q0 + m[4] * q1 + m[8] * q2 + m[12];
  p[1] = m[1] * q0 + m[5] * q1 + m[9] * q2 + m[13];
  p[2] = m[2] * q0 + m[6] * q1 + m[10] * q2 + m[14];
  p[3] = m[3] * q0 + m[7] * q1 + m[11] * q2 + m[15];
}


/*========================================================================*/
void MatrixInvTransformC44fAs33f3f(float *m, float *q, float *p)
{
  /* multiplying a column major rotation matrix as row-major will
   * give the inverse rotation */
  register float q0 = *q, q1 = *(q + 1), q2 = *(q + 2);
  p[0] = m[0] * q0 + m[1] * q1 + m[2] * q2;
  p[1] = m[4] * q0 + m[5] * q1 + m[6] * q2;
  p[2] = m[8] * q0 + m[9] * q1 + m[10] * q2;
}


/*========================================================================*/
void MatrixTransformC44fAs33f3f(float *m, float *q, float *p)
{
  register float q0 = *q, q1 = *(q + 1), q2 = *(q + 2);
  p[0] = m[0] * q0 + m[4] * q1 + m[8] * q2;
  p[1] = m[1] * q0 + m[5] * q1 + m[9] * q2;
  p[2] = m[2] * q0 + m[6] * q1 + m[10] * q2;
}


/*========================================================================*/
float MatrixGetRMS(PyMOLGlobals * G, int n, float *v1, float *v2, float *wt)
{
  /* Just Compute RMS given current coordinates */

  float *vv1, *vv2;
  float err, etmp, tmp;
  int a, c;
  float sumwt = 0.0F;

  if(wt) {
    for(c = 0; c < n; c++)
      if(wt[c] != 0.0F) {
        sumwt = sumwt + wt[c];
      }
  } else {
    for(c = 0; c < n; c++)
      sumwt += 1.0F;
  }
  err = 0.0F;
  vv1 = v1;
  vv2 = v2;
  for(c = 0; c < n; c++) {
    etmp = 0.0F;
    for(a = 0; a < 3; a++) {
      tmp = (vv2[a] - vv1[a]);
      etmp += tmp * tmp;
    }
    if(wt)
      err += wt[c] * etmp;
    else
      err += etmp;
    vv1 += 3;
    vv2 += 3;
  }
  err = err / sumwt;
  err = (float) sqrt1f(err);

  if(fabs(err) < R_SMALL4)
    err = 0.0F;

  return (err);
}


/*========================================================================*/
float MatrixFitRMSTTTf(PyMOLGlobals * G, int n, float *v1, float *v2, float *wt,
                       float *ttt)
{
  /*
     Subroutine to do the actual RMS fitting of two sets of vector coordinates
     This routine does not rotate the actual coordinates, but instead returns 
     the RMS fitting value, along with the center-of-mass translation vectors 
     T1 and T2 and the rotation matrix M, which rotates the translated 
     coordinates of molecule 2 onto the translated coordinates of molecule 1.
   */

  double m[3][3], aa[3][3];
  double sumwt, tol;
  int a, b, c, maxiter;
  double t1[3], t2[3];

  /* special case: just one atom pair */

  if(n == 1) {
    if(ttt) {
      for(a = 1; a < 11; a++)
        ttt[a] = 0.0F;
      for(a = 0; a < 12; a += 5)
        ttt[a] = 1.0F;
      for(a = 0; a < 3; a++)
        ttt[a + 12] = v2[a] - v1[a];
    }
    return 0.0F;
  }

  /* Initialize arrays. */

  for(a = 0; a < 3; a++) {
    for(b = 0; b < 3; b++) {
      aa[a][b] = 0.0;
    }
    t1[a] = 0.0;
    t2[a] = 0.0;
  }

  sumwt = 0.0F;
  tol = SettingGetGlobal_f(G, cSetting_fit_tolerance);
  maxiter = SettingGetGlobal_i(G, cSetting_fit_iterations);

  /* Calculate center-of-mass vectors */

  {
    float *vv1 = v1, *vv2 = v2;

    if(wt) {
      for(c = 0; c < n; c++) {
        for(a = 0; a < 3; a++) {
          t1[a] += wt[c] * vv1[a];
          t2[a] += wt[c] * vv2[a];
        }
        if(wt[c] != 0.0F) {
          sumwt = sumwt + wt[c];
        } else {
          sumwt = sumwt + 1.0F; /* WHAT IS THIS? */
        }
        vv1 += 3;
        vv2 += 3;
      }
    } else {
      for(c = 0; c < n; c++) {
        for(a = 0; a < 3; a++) {
          t1[a] += vv1[a];
          t2[a] += vv2[a];
        }
        sumwt += 1.0F;
        vv1 += 3;
        vv2 += 3;
      }
    }
    if(sumwt == 0.0F)
      sumwt = 1.0F;
    for(a = 0; a < 3; a++) {
      t1[a] /= sumwt;
      t2[a] /= sumwt;
    }
  }

  {
    /* Calculate correlation matrix */
    double x[3], xx[3];
    float *vv1 = v1, *vv2 = v2;
    for(c = 0; c < n; c++) {
      if(wt) {
        for(a = 0; a < 3; a++) {
          x[a] = wt[c] * (vv1[a] - t1[a]);
          xx[a] = wt[c] * (vv2[a] - t2[a]);
        }
      } else {
        for(a = 0; a < 3; a++) {
          x[a] = vv1[a] - t1[a];
          xx[a] = vv2[a] - t2[a];
        }
      }
      for(a = 0; a < 3; a++)
        for(b = 0; b < 3; b++)
          aa[a][b] = aa[a][b] + xx[a] * x[b];
      vv1 += 3;
      vv2 += 3;
    }
  }

  if(n > 1) {
    int got_kabsch = false;
    int fit_kabsch = SettingGetGlobal_i(G, cSetting_fit_kabsch);
    if(fit_kabsch) {

      /* WARNING: Kabsch isn't numerically stable */

      /* Kabsch as per

         http://en.wikipedia.org/wiki/Kabsch_algorithm

         minimal RMS matrix is (AtA)^(1/2) * A_inverse, where

         Aij =  Pki Qkj

         assuming Pki and Qkj are centered about the same origin.

       */

      /* NOTE: This Kabsch implementation only works with 4 or more atoms */

      double At[3][3], AtA[3][3];

      /* compute At and At * A */

      transpose33d33d((double *) (void *) aa, (double *) (void *) At);

      multiply33d33d((double *) (void *) At, (double *) (void *) aa,
                     (double *) (void *) AtA);

      /* solve A*At (a real symmetric matrix) */

      {
        double e_vec[3][3], e_val[3];
        xx_word n_rot;

        if(xx_matrix_jacobi_solve((xx_float64 *) (void *) e_vec,
                                  (xx_float64 *) (void *) e_val,
                                  &n_rot, (xx_float64 *) (void *) AtA, 3)) {
          double V[3][3], Vt[3][3];

          /* Kabsch requires non-negative eigenvalues (since sqrt is taken) */

          if((e_val[0] >= 0.0) && (e_val[1] >= 0.0) && (e_val[2] >= 0.0)) {
            switch (fit_kabsch) {
            case 1:
              {

                /* original Kabsch performs an unnecessary matrix inversion */

                /* rot matrix = (AtA)^(1/2) * A^(-1) */

                double rootD[3][3], sqrtAtA[3][3], Ai[3][3];

                for(a = 0; a < 3; a++)
                  for(b = 0; b < 3; b++) {
                    if(a == b) {
                      rootD[a][b] = sqrt1d(e_val[a]);
                    } else {
                      rootD[a][b] = 0.0;
                    }
                    V[a][b] = e_vec[a][b];
                    Vt[a][b] = e_vec[b][a];
                  }

                multiply33d33d((double *) (void *) rootD, (double *) (void *) Vt,
                               (double *) (void *) sqrtAtA);
                multiply33d33d((double *) (void *) V, (double *) (void *) sqrtAtA,
                               (double *) (void *) sqrtAtA);
                /* compute Ai */

                if(xx_matrix_invert((xx_float64 *) (void *) Ai,
                                    (xx_float64 *) (void *) aa, 3)) {

                  /* now compute the rotation matrix  = (AtA)^(1/2) * Ai */

                  multiply33d33d((double *) (void *) sqrtAtA,
                                 (double *) (void *) Ai, (double *) (void *) m);

                  got_kabsch = true;

                  {             /* is the rotation matrix left-handed? Then swap the
                                   recomposition so as to avoid the reflection */
                    double cp[3], dp;
                    cross_product3d((double *) (void *) m, (double *) (void *) m + 3, cp);
                    dp = dot_product3d((double *) (void *) m + 6, cp);
                    if((1.0 - fabs(dp)) > R_SMALL4) {   /* not orthonormal? */
                      got_kabsch = false;

                      PRINTFB(G, FB_Matrix, FB_Warnings)
                        "Matrix-Warning: Kabsch matrix not orthonormal: falling back on iteration.\n"
                        ENDFB(G);

                    } else if(dp < 0.0F) {
                      multiply33d33d((double *) (void *) rootD, (double *) (void *) V,
                                     (double *) (void *) sqrtAtA);
                      multiply33d33d((double *) (void *) Vt, (double *) (void *) sqrtAtA,
                                     (double *) (void *) sqrtAtA);
                      multiply33d33d((double *) (void *) sqrtAtA, (double *) (void *) Ai,
                                     (double *) (void *) m);
                    }
                  }
                } else {
                  PRINTFB(G, FB_Matrix, FB_Warnings)
                    "Matrix-Warning: Kabsch matrix inversion failed: falling back on iteration.\n"
                    ENDFB(G);
                }
              }
              break;
            case 2:
              {
                /* improved Kabsch skips the matrix inversion */

                if((e_val[0] > R_SMALL8) &&
                   (e_val[1] > R_SMALL8) && (e_val[2] > R_SMALL8)) {

                  /* inv rot matrix = U Vt = A V D^(-1/2) Vt
                   * where U from SVD of A = U S Vt 
                   * and where U is known to be = A V D^(-1/2)
                   * where D are eigenvalues of AtA */

                  double invRootD[3][3], Mi[3][3];

                  for(a = 0; a < 3; a++)
                    for(b = 0; b < 3; b++) {
                      if(a == b) {
                        invRootD[a][b] = 1.0 / sqrt1d(e_val[a]);
                      } else {
                        invRootD[a][b] = 0.0;
                      }
                      V[a][b] = e_vec[a][b];
                      Vt[a][b] = e_vec[b][a];
                    }

                  /* now compute the rotation matrix directly  */

                  multiply33d33d((double *) (void *) invRootD, (double *) (void *) Vt,
                                 (double *) (void *) Mi);
                  multiply33d33d((double *) (void *) V, (double *) (void *) Mi,
                                 (double *) (void *) Mi);
                  multiply33d33d((double *) (void *) aa, (double *) (void *) Mi,
                                 (double *) (void *) Mi);

                  got_kabsch = true;

                  {             /* cis the rotation matrix left-handed? Then swap the
                                   recomposition so as to avoid the reflection */
                    double cp[3], dp;
                    cross_product3d((double *) (void *) Mi, (double *) (void *) Mi + 3,
                                    cp);
                    dp = dot_product3d((double *) (void *) Mi + 6, cp);
                    if((1.0 - fabs(dp)) > R_SMALL4) {   /* not orthonormal? */
                      got_kabsch = false;

                      PRINTFB(G, FB_Matrix, FB_Warnings)
                        "Matrix-Warning: Kabsch matrix not orthonormal: falling back on iteration.\n"
                        ENDFB(G);

                    } else if(dp < 0.0F) {
                      multiply33d33d((double *) (void *) invRootD, (double *) (void *) V,
                                     (double *) (void *) Mi);
                      multiply33d33d((double *) (void *) Vt, (double *) (void *) Mi,
                                     (double *) (void *) Mi);
                      multiply33d33d((double *) (void *) aa, (double *) (void *) Mi,
                                     (double *) (void *) Mi);
                    }
                  }

                  if(got_kabsch) {      /* transpose to get the inverse */
                    transpose33d33d((double *) (void *) Mi, (double *) (void *) m);
                  }

                } else {
                  PRINTFB(G, FB_Matrix, FB_Warnings)
                    "Matrix-Warning: Kabsch matrix degenerate: falling back on iteration.\n"
                    ENDFB(G);
                }
              }
              break;
            }

            /* validate the result */

            if(got_kabsch) {

              if((fabs(length3d(m[0]) - 1.0) < R_SMALL4) &&
                 (fabs(length3d(m[1]) - 1.0) < R_SMALL4) &&
                 (fabs(length3d(m[2]) - 1.0) < R_SMALL4)) {

                recondition33d((double *) (void *) m);

              } else {
                got_kabsch = false;

                PRINTFB(G, FB_Matrix, FB_Warnings)
                  "Matrix-Warning: Kabsch matrix not normal: falling back on iteration.\n"
                  ENDFB(G);
              }
            }
          } else {
            PRINTFB(G, FB_Matrix, FB_Warnings)
              "Matrix-Warning: Kabsch eigenvalue(s) negative: falling back on iteration.\n"
              ENDFB(G);
          }
        } else {
          PRINTFB(G, FB_Matrix, FB_Warnings)
            "Matrix-Warning: Kabsch decomposition failed: falling back on iteration.\n"
            ENDFB(G);
        }
      }
    }

    if(!got_kabsch) {

      /* use PyMOL's original iteration algorithm if Kabsch is
         disabled or fails (quite common). */

      /* Primary iteration scheme to determine rotation matrix for molecule 2 */
      double sg, bb, cc;
      int iters, ix, iy, iz, unchanged = 0;
      double sig, gam;
      double tmp;
      double save[3][3];
      int perturbed = false;

      for(a = 0; a < 3; a++) {
        for(b = 0; b < 3; b++) {
          m[a][b] = 0.0;
          save[a][b] = aa[a][b];
        }
        m[a][a] = 1.0;
      }

      iters = 0;
      while(1) {

        /* IX, IY, and IZ rotate 1-2-3, 2-3-1, 3-1-2, etc. */
        iz = (iters + 1) % 3;
        iy = (iz + 1) % 3;
        ix = (iy + 1) % 3;
        sig = aa[iz][iy] - aa[iy][iz];
        gam = aa[iy][iy] + aa[iz][iz];

        if(iters >= maxiter) {
          PRINTFB(G, FB_Matrix, FB_Details)
            " Matrix: Warning: no convergence (%1.8f<%1.8f after %d iterations).\n",
            (float) tol, (float) gam, iters ENDFB(G);
          break;
        }

        /* Determine size of off-diagonal element.  If off-diagonals exceed the
           diagonal elements tolerance, perform Jacobi rotation. */
        tmp = sig * sig + gam * gam;
        sg = sqrt1d(tmp);
        if((sg != 0.0F) && (fabs(sig) > (tol * fabs(gam)))) {
          unchanged = 0;
          sg = 1.0F / sg;
          for(a = 0; a < 3; a++) {
            bb = gam * aa[iy][a] + sig * aa[iz][a];
            cc = gam * aa[iz][a] - sig * aa[iy][a];
            aa[iy][a] = bb * sg;
            aa[iz][a] = cc * sg;

            bb = gam * m[iy][a] + sig * m[iz][a];
            cc = gam * m[iz][a] - sig * m[iy][a];
            m[iy][a] = bb * sg;
            m[iz][a] = cc * sg;
          }
        } else {
          unchanged++;
          if(unchanged == 3) {
            double residual = 0.0;
            for(a = 0; a < 3; a++) {
              for(b = 0; b < 3; b++) {
                residual += fabs(aa[a][b] - save[a][b]);
              }
            }
            if(residual > R_SMALL4) {
              /* matrix has changed significantly, so we assume that
                 we found the minimum */
              break;
            } else if(perturbed) {
              /* we ended up back where we started even after perturbing */
              break;
            } else {            /* hmm...no change from start... so displace 90
                                   degrees just to make sure we didn't start out
                                   trapped in precisely the opposite direction */
              for(a = 0; a < 3; a++) {
                bb = aa[iz][a];
                cc = -aa[iy][a];
                aa[iy][a] = bb;
                aa[iz][a] = cc;

                bb = m[iz][a];
                cc = -m[iy][a];
                m[iy][a] = bb;
                m[iz][a] = cc;
              }
              perturbed = true;
              unchanged = 0;
            }
            /* only give up if we've iterated through all three planes */
          }
        }
        iters++;
      }
      recondition33d((double *) (void *) m);
    }
  }

  /* At this point, we should have a converged rotation matrix (M).  Calculate
     the weighted RMS error. */
  {
    float *vv1 = v1, *vv2 = v2;
    double etmp, tmp;
    double err = 0.0;
    for(c = 0; c < n; c++) {
      etmp = 0.0;
      for(a = 0; a < 3; a++) {
        tmp = m[a][0] * (vv2[0] - t2[0])
          + m[a][1] * (vv2[1] - t2[1])
          + m[a][2] * (vv2[2] - t2[2]);
        tmp = (vv1[a] - t1[a]) - tmp;
        etmp += tmp * tmp;
      }
      if(wt)
        err += wt[c] * etmp;
      else
        err += etmp;
      vv1 += 3;
      vv2 += 3;
    }

    err = err / sumwt;
    err = sqrt1d(err);

    /* NOTE: TTT's are now row-major (to be more like homogenous matrices) */

    if(ttt) {
      ttt[0] = (float) m[0][0];
      ttt[1] = (float) m[1][0];
      ttt[2] = (float) m[2][0];
      ttt[3] = (float) t2[0];
      ttt[4] = (float) m[0][1];
      ttt[5] = (float) m[1][1];
      ttt[6] = (float) m[2][1];
      ttt[7] = (float) t2[1];
      ttt[8] = (float) m[0][2];
      ttt[9] = (float) m[1][2];
      ttt[10] = (float) m[2][2];
      ttt[11] = (float) t2[2];
      ttt[12] = (float) -t1[0];
      ttt[13] = (float) -t1[1];
      ttt[14] = (float) -t1[2];
    }
    /* for compatibility with normal 4x4 matrices */

    if(fabs(err) < R_SMALL4)
      err = 0.0F;

    return ((float) err);
  }
}


/*========================================================================*/


/*========================================================================*/


/*========================================================================*/


/*========================================================================*/


/*========================================================================*/


/*========================================================================*/


/*========================================================================*/


/* Only a partial translation of eispack -
 * just the real general diagonialization and support routines */


/* eispack.f -- translated by f2c (version 19970805).*/

typedef unsigned int uinteger;
typedef char *address;
typedef short int shortint;
typedef float real;
typedef struct {
  real r, i;
} complex;
typedef struct {
  doublereal r, i;
} doublecomplex;
typedef int logical;
typedef short int shortlogical;
typedef char logical1;
typedef char integer1;

#define TRUE_ (1)
#define FALSE_ (0)


/* Extern is for use with -E */
#ifndef Extern
#define Extern extern
#endif


/* I/O stuff */

#ifdef f2c_i2


/* for -i2 */
typedef short flag;
typedef short ftnlen;
typedef short ftnint;
#else
typedef long int flag;
typedef long int ftnlen;
typedef long int ftnint;
#endif

#define VOID void

#define abs(x) ((x) >= 0 ? (x) : -(x))
#define dabs(x) (doublereal)abs(x)
#define mymin(a,b) ((a) <= (b) ? (a) : (b))
#define mymax(a,b) ((a) >= (b) ? (a) : (b))
#define dmymin(a,b) (doublereal)mymin(a,b)
#define dmymax(a,b) (doublereal)mymax(a,b)
#define bit_test(a,b)	((a) >> (b) & 1)
#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))


/*========================================================================*/

int MatrixEigensolveC33d(PyMOLGlobals * G, double *a, double *wr, double *wi, double *v)
{
  integer n, nm;
  integer iv1[3];
  integer matz;
  double fv1[9];
  double at[9];
  integer ierr;
  int x;

  nm = 3;
  n = 3;
  matz = 1;

  for(x = 0; x < 9; x++)        /* make a copy -- eispack trashes the matrix */
    at[x] = a[x];

  pymol_rg_(&nm, &n, at, wr, wi, &matz, v, iv1, fv1, &ierr);

  /* NOTE: the returned eigenvectors are stored one per row which is
     is actually the inverse of the normal eigenvalue matrix -
     ----
     IS that because we're actually solving the transpose?
   */

  if(Feedback(G, FB_Matrix, FB_Blather)) {
    printf(" Eigensolve: eigenvectors %8.3f %8.3f %8.3f\n", v[0], v[1], v[2]);
    printf(" Eigensolve:              %8.3f %8.3f %8.3f\n", v[3], v[4], v[5]);
    printf(" Eigensolve:              %8.3f %8.3f %8.3f\n", v[6], v[7], v[8]);

    printf(" Eigensolve: eigenvalues  %8.3f %8.3f %8.3f\n", wr[0], wr[1], wr[2]);
    printf(" Eigensolve:              %8.3f %8.3f %8.3f\n", wi[0], wi[1], wi[2]);
  }
  return (ierr);
}

int MatrixEigensolveC44d(PyMOLGlobals * G, double *a, double *wr, double *wi, double *v)
{
  integer n, nm;
  integer iv1[4];
  integer matz;
  double fv1[16];
  double at[16];
  integer ierr;
  int x;

  nm = 4;
  n = 4;
  matz = 1;

  for(x = 0; x < 16; x++)       /* make a copy */
    at[x] = a[x];

  pymol_rg_(&nm, &n, at, wr, wi, &matz, v, iv1, fv1, &ierr);

  /* NOTE: the returned eigenvectors are stored one per row */

  if(Feedback(G, FB_Matrix, FB_Blather)) {
    printf(" Eigensolve: eigenvectors %8.3f %8.3f %8.3f %8.3f\n", v[0], v[1], v[2], v[3]);
    printf(" Eigensolve:              %8.3f %8.3f %8.3f %8.3f\n", v[4], v[5], v[6], v[7]);
    printf(" Eigensolve:              %8.3f %8.3f %8.3f %8.3f\n", v[8], v[9], v[10],
           v[11]);
    printf(" Eigensolve:              %8.3f %8.3f %8.3f %8.3f\n", v[12], v[13], v[14],
           v[15]);

    printf(" Eigensolve: eigenvalues  %8.3f %8.3f %8.3f %8.3f\n", wr[0], wr[1], wr[2],
           wr[3]);
    printf(" Eigensolve:              %8.3f %8.3f %8.3f %8.3f\n", wi[0], wi[1], wi[2],
           wi[3]);
  }

  return (ierr);
}

static double d_sign(doublereal * a, doublereal * b);

static int balanc_(integer * nm, integer * n, doublereal * a, integer * low,
                   integer * igh, doublereal * scale);

static int balbak_(integer * nm, integer * n, integer * low, integer * igh,
                   doublereal * scale, integer * m, doublereal * z__);

static int cdiv_(doublereal * ar, doublereal * ai, doublereal * br, doublereal * bi,
                 doublereal * cr, doublereal * ci);

static int elmhes_(integer * nm, integer * n, integer * low, integer * igh,
                   doublereal * a, integer * int__);

static int eltran_(integer * nm, integer * n, integer * low, integer * igh,
                   doublereal * a, integer * int__, doublereal * z__);

static int hqr2_(integer * nm, integer * n, integer * low, integer * igh,
                 doublereal * h__, doublereal * wr, doublereal * wi, doublereal * z__,
                 integer * ierr);

static int hqr_(integer * nm, integer * n, integer * low, integer * igh,
                doublereal * h__, doublereal * wr, doublereal * wi, integer * ierr);

double d_sign(doublereal * a, doublereal * b)
{
  double x;
  x = (*a >= 0 ? *a : -*a);
  return (*b >= 0 ? x : -x);
}


/* Table of constant values */

static doublereal c_b126 = 0.;

static int balanc_(integer * nm, integer * n, doublereal * a, integer * low,
                       integer * igh, doublereal * scale)
{


/* System generated locals */
  integer a_dim1, a_offset, i__1, i__2;
  doublereal d__1;


/* Local variables */
  integer iexc;
  doublereal c__, f, g;
  integer i__, j, k, l, m;
  doublereal r__, s, radix, b2;
  integer jj;
  logical noconv;


/*     this subroutine is a translation of the algol procedure balance, */


/*     num. math. 13, 293-304(1969) by parlett and reinsch. */


/*     handbook for auto. comp., vol.ii-linear algebra, 315-326(1971). */


/*     this subroutine balances a real matrix and isolates */


/*     eigenvalues whenever possible. */


/*     on input */


/*        nm must be set to the row dimension of two-dimensional */


/*          array parameters as declared in the calling program */


/*          dimension statement. */


/*        n is the order of the matrix. */


/*        a contains the input matrix to be balanced. */


/*     on output */


/*        a contains the balanced matrix. */


/*        low and igh are two integers such that a(i,j) */


/*          is equal to zero if */


/*           (1) i is greater than j and */


/*           (2) j=1,...,low-1 or i=igh+1,...,n. */


/*        scale contains information determining the */


/*           permutations and scaling factors used. */


/*     suppose that the principal submatrix in rows low through igh */


/*     has been balanced, that p(j) denotes the index interchanged */


/*     with j during the permutation step, and that the elements */


/*     of the diagonal matrix used are denoted by d(i,j).  then */


/*        scale(j) = p(j),    for j = 1,...,low-1 */


/*                 = d(j,j),      j = low,...,igh */


/*                 = p(j)         j = igh+1,...,n. */


/*     the order in which the interchanges are made is n to igh+1, */


/*     then 1 to low-1. */


/*     note that 1 is returned for igh if igh is zero formally. */


/*     the algol procedure exc contained in balance appears in */


/*     balanc  in line.  (note that the algol roles of identifiers */


/*     k,l have been reversed.) */


/*     questions and comments should be directed to burton s. garbow, */


/*     mathematics and computer science div, argonne national laboratory 
*/


/*     this version dated august 1983. */


/*     ------------------------------------------------------------------ 
*/


/* Parameter adjustments */
  --scale;
  a_dim1 = *nm;
  a_offset = a_dim1 + 1;
  a -= a_offset;


/* Function Body */
  radix = 16.;

  b2 = radix * radix;
  k = 1;
  l = *n;
  goto L100;


/*     .......... in-line procedure for row and */


/*                column exchange .......... */
L20:
  scale[m] = (doublereal) j;
  if(j == m) {
    goto L50;
  }

  i__1 = l;
  for(i__ = 1; i__ <= i__1; ++i__) {
    f = a[i__ + j * a_dim1];
    a[i__ + j * a_dim1] = a[i__ + m * a_dim1];
    a[i__ + m * a_dim1] = f;


/* L30: */
  }

  i__1 = *n;
  for(i__ = k; i__ <= i__1; ++i__) {
    f = a[j + i__ * a_dim1];
    a[j + i__ * a_dim1] = a[m + i__ * a_dim1];
    a[m + i__ * a_dim1] = f;


/* L40: */
  }

L50:
  switch ((int) iexc) {
  case 1:
    goto L80;
  case 2:
    goto L130;
  }


/*     .......... search for rows isolating an eigenvalue */


/*                and push them down .......... */
L80:
  if(l == 1) {
    goto L280;
  }
  --l;


/*     .......... for j=l step -1 until 1 do -- .......... */
L100:
  i__1 = l;
  for(jj = 1; jj <= i__1; ++jj) {
    j = l + 1 - jj;

    i__2 = l;
    for(i__ = 1; i__ <= i__2; ++i__) {
      if(i__ == j) {
        goto L110;
      }
      if(a[j + i__ * a_dim1] != 0.) {
        goto L120;
      }
    L110:
      ;
    }

    m = l;
    iexc = 1;
    goto L20;
  L120:
    ;
  }

  goto L140;


/*     .......... search for columns isolating an eigenvalue */


/*                and push them left .......... */
L130:
  ++k;

L140:
  i__1 = l;
  for(j = k; j <= i__1; ++j) {

    i__2 = l;
    for(i__ = k; i__ <= i__2; ++i__) {
      if(i__ == j) {
        goto L150;
      }
      if(a[i__ + j * a_dim1] != 0.) {
        goto L170;
      }
    L150:
      ;
    }

    m = k;
    iexc = 2;
    goto L20;
  L170:
    ;
  }


/*     .......... now balance the submatrix in rows k to l .......... */
  i__1 = l;
  for(i__ = k; i__ <= i__1; ++i__) {


/* L180: */
    scale[i__] = 1.;
  }


/*     .......... iterative loop for norm reduction .......... */
L190:
  noconv = FALSE_;

  i__1 = l;
  for(i__ = k; i__ <= i__1; ++i__) {
    c__ = 0.;
    r__ = 0.;

    i__2 = l;
    for(j = k; j <= i__2; ++j) {
      if(j == i__) {
        goto L200;
      }
      c__ += (d__1 = a[j + i__ * a_dim1], abs(d__1));
      r__ += (d__1 = a[i__ + j * a_dim1], abs(d__1));
    L200:
      ;
    }


/*     .......... guard against zero c or r due to underflow .........
. */
    if(c__ == 0. || r__ == 0.) {
      goto L270;
    }
    g = r__ / radix;
    f = 1.;
    s = c__ + r__;
  L210:
    if(c__ >= g) {
      goto L220;
    }
    f *= radix;
    c__ *= b2;
    goto L210;
  L220:
    g = r__ * radix;
  L230:
    if(c__ < g) {
      goto L240;
    }
    f /= radix;
    c__ /= b2;
    goto L230;


/*     .......... now balance .......... */
  L240:
    if((c__ + r__) / f >= s * .95) {
      goto L270;
    }
    g = 1. / f;
    scale[i__] *= f;
    noconv = TRUE_;

    i__2 = *n;
    for(j = k; j <= i__2; ++j) {


/* L250: */
      a[i__ + j * a_dim1] *= g;
    }

    i__2 = l;
    for(j = 1; j <= i__2; ++j) {


/* L260: */
      a[j + i__ * a_dim1] *= f;
    }

  L270:
    ;
  }

  if(noconv) {
    goto L190;
  }

L280:
  *low = k;
  *igh = l;
  return 0;
}                               /* balanc_ */

static int balbak_(integer * nm, integer * n, integer * low, integer * igh,
                   doublereal * scale, integer * m, doublereal * z__)
{


/* System generated locals */
  integer z_dim1, z_offset, i__1, i__2;


/* Local variables */
  integer i__, j, k;
  doublereal s;
  integer ii;


/*     this subroutine is a translation of the algol procedure balbak, */


/*     num. math. 13, 293-304(1969) by parlett and reinsch. */


/*     handbook for auto. comp., vol.ii-linear algebra, 315-326(1971). */


/*     this subroutine forms the eigenvectors of a real general */


/*     matrix by back transforming those of the corresponding */


/*     balanced matrix determined by  balanc. */


/*     on input */


/*        nm must be set to the row dimension of two-dimensional */


/*          array parameters as declared in the calling program */


/*          dimension statement. */


/*        n is the order of the matrix. */


/*        low and igh are integers determined by  balanc. */


/*        scale contains information determining the permutations */


/*          and scaling factors used by  balanc. */


/*        m is the number of columns of z to be back transformed. */


/*        z contains the real and imaginary parts of the eigen- */


/*          vectors to be back transformed in its first m columns. */


/*     on output */


/*        z contains the real and imaginary parts of the */


/*          transformed eigenvectors in its first m columns. */


/*     questions and comments should be directed to burton s. garbow, */


/*     mathematics and computer science div, argonne national laboratory 
*/


/*     this version dated august 1983. */


/*     ------------------------------------------------------------------ 
*/


/* Parameter adjustments */
  --scale;
  z_dim1 = *nm;
  z_offset = z_dim1 + 1;
  z__ -= z_offset;


/* Function Body */
  if(*m == 0) {
    goto L200;
  }
  if(*igh == *low) {
    goto L120;
  }

  i__1 = *igh;
  for(i__ = *low; i__ <= i__1; ++i__) {
    s = scale[i__];


/*     .......... left hand eigenvectors are back transformed */


/*                if the foregoing statement is replaced by */


/*                s=1.0d0/scale(i). .......... */
    i__2 = *m;
    for(j = 1; j <= i__2; ++j) {


/* L100: */
      z__[i__ + j * z_dim1] *= s;
    }


/* L110: */
  }


/*     ......... for i=low-1 step -1 until 1, */


/*               igh+1 step 1 until n do -- .......... */
L120:
  i__1 = *n;
  for(ii = 1; ii <= i__1; ++ii) {
    i__ = ii;
    if(i__ >= *low && i__ <= *igh) {
      goto L140;
    }
    if(i__ < *low) {
      i__ = *low - ii;
    }
    k = (integer) scale[i__];
    if(k == i__) {
      goto L140;
    }

    i__2 = *m;
    for(j = 1; j <= i__2; ++j) {
      s = z__[i__ + j * z_dim1];
      z__[i__ + j * z_dim1] = z__[k + j * z_dim1];
      z__[k + j * z_dim1] = s;


/* L130: */
    }

  L140:
    ;
  }

L200:
  return 0;
}                               /* balbak_ */

static int cdiv_(doublereal * ar, doublereal * ai, doublereal * br, doublereal * bi,
                 doublereal * cr, doublereal * ci)
{


/* System generated locals */
  doublereal d__1, d__2;


/* Local variables */
  doublereal s, ais, bis, ars, brs;


/*     complex division, (cr,ci) = (ar,ai)/(br,bi) */

  s = abs(*br) + abs(*bi);
  ars = *ar / s;
  ais = *ai / s;
  brs = *br / s;
  bis = *bi / s;


/* Computing 2nd power */
  d__1 = brs;


/* Computing 2nd power */
  d__2 = bis;
  s = d__1 * d__1 + d__2 * d__2;
  *cr = (ars * brs + ais * bis) / s;
  *ci = (ais * brs - ars * bis) / s;
  return 0;
}                               /* cdiv_ */

static int elmhes_(integer * nm, integer * n, integer * low, integer * igh,
                   doublereal * a, integer * int__)
{


/* System generated locals */
  integer a_dim1, a_offset, i__1, i__2, i__3;
  doublereal d__1;


/* Local variables */
  integer i__, j, m;
  doublereal x, y;
  integer la, mm1, kp1, mp1;


/*     this subroutine is a translation of the algol procedure elmhes, */


/*     num. math. 12, 349-368(1968) by martin and wilkinson. */


/*     handbook for auto. comp., vol.ii-linear algebra, 339-358(1971). */


/*     given a real general matrix, this subroutine */


/*     reduces a submatrix situated in rows and columns */


/*     low through igh to upper hessenberg form by */


/*     stabilized elementary similarity transformations. */


/*     on input */


/*        nm must be set to the row dimension of two-dimensional */


/*          array parameters as declared in the calling program */


/*          dimension statement. */


/*        n is the order of the matrix. */


/*        low and igh are integers determined by the balancing */


/*          subroutine  balanc.  if  balanc  has not been used, */


/*          set low=1, igh=n. */


/*        a contains the input matrix. */


/*     on output */


/*        a contains the hessenberg matrix.  the multipliers */


/*          which were used in the reduction are stored in the */


/*          remaining triangle under the hessenberg matrix. */


/*        int contains information on the rows and columns */


/*          interchanged in the reduction. */


/*          only elements low through igh are used. */


/*     questions and comments should be directed to burton s. garbow, */


/*     mathematics and computer science div, argonne national laboratory 
*/


/*     this version dated august 1983. */


/*     ------------------------------------------------------------------ 
*/


/* Parameter adjustments */
  a_dim1 = *nm;
  a_offset = a_dim1 + 1;
  a -= a_offset;
  --int__;


/* Function Body */
  la = *igh - 1;
  kp1 = *low + 1;
  if(la < kp1) {
    goto L200;
  }

  i__1 = la;
  for(m = kp1; m <= i__1; ++m) {
    mm1 = m - 1;
    x = 0.;
    i__ = m;

    i__2 = *igh;
    for(j = m; j <= i__2; ++j) {
      if((d__1 = a[j + mm1 * a_dim1], abs(d__1)) <= abs(x)) {
        goto L100;
      }
      x = a[j + mm1 * a_dim1];
      i__ = j;
    L100:
      ;
    }

    int__[m] = i__;
    if(i__ == m) {
      goto L130;
    }


/*     .......... interchange rows and columns of a .......... */
    i__2 = *n;
    for(j = mm1; j <= i__2; ++j) {
      y = a[i__ + j * a_dim1];
      a[i__ + j * a_dim1] = a[m + j * a_dim1];
      a[m + j * a_dim1] = y;


/* L110: */
    }

    i__2 = *igh;
    for(j = 1; j <= i__2; ++j) {
      y = a[j + i__ * a_dim1];
      a[j + i__ * a_dim1] = a[j + m * a_dim1];
      a[j + m * a_dim1] = y;


/* L120: */
    }


/*     .......... end interchange .......... */
  L130:
    if(x == 0.) {
      goto L180;
    }
    mp1 = m + 1;

    i__2 = *igh;
    for(i__ = mp1; i__ <= i__2; ++i__) {
      y = a[i__ + mm1 * a_dim1];
      if(y == 0.) {
        goto L160;
      }
      y /= x;
      a[i__ + mm1 * a_dim1] = y;

      i__3 = *n;
      for(j = m; j <= i__3; ++j) {


/* L140: */
        a[i__ + j * a_dim1] -= y * a[m + j * a_dim1];
      }

      i__3 = *igh;
      for(j = 1; j <= i__3; ++j) {


/* L150: */
        a[j + m * a_dim1] += y * a[j + i__ * a_dim1];
      }

    L160:
      ;
    }

  L180:
    ;
  }

L200:
  return 0;
}                               /* elmhes_ */

static int eltran_(integer * nm, integer * n, integer * low, integer * igh,
                   doublereal * a, integer * int__, doublereal * z__)
{
  /* System generated locals */
  integer a_dim1, a_offset, z_dim1, z_offset, i__1, i__2;

  /* Local variables */
  integer i__, j, kl, mm, mp, mp1;


/*     this subroutine is a translation of the algol procedure elmtrans, 
*/


/*     num. math. 16, 181-204(1970) by peters and wilkinson. */


/*     handbook for auto. comp., vol.ii-linear algebra, 372-395(1971). */


/*     this subroutine accumulates the stabilized elementary */


/*     similarity transformations used in the reduction of a */


/*     real general matrix to upper hessenberg form by  elmhes. */


/*     on input */


/*        nm must be set to the row dimension of two-dimensional */


/*          array parameters as declared in the calling program */


/*          dimension statement. */


/*        n is the order of the matrix. */


/*        low and igh are integers determined by the balancing */


/*          subroutine  balanc.  if  balanc  has not been used, */


/*          set low=1, igh=n. */


/*        a contains the multipliers which were used in the */


/*          reduction by  elmhes  in its lower triangle */


/*          below the subdiagonal. */


/*        int contains information on the rows and columns */


/*          interchanged in the reduction by  elmhes. */


/*          only elements low through igh are used. */


/*     on output */


/*        z contains the transformation matrix produced in the */


/*          reduction by  elmhes. */


/*     questions and comments should be directed to burton s. garbow, */


/*     mathematics and computer science div, argonne national laboratory 
*/


/*     this version dated august 1983. */


/*     ------------------------------------------------------------------ 
*/


/*     .......... initialize z to identity matrix .......... */
  /* Parameter adjustments */
  z_dim1 = *nm;
  z_offset = z_dim1 + 1;
  z__ -= z_offset;
  --int__;
  a_dim1 = *nm;
  a_offset = a_dim1 + 1;
  a -= a_offset;

  /* Function Body */
  i__1 = *n;
  for(j = 1; j <= i__1; ++j) {

    i__2 = *n;
    for(i__ = 1; i__ <= i__2; ++i__) {


/* L60: */
      z__[i__ + j * z_dim1] = 0.;
    }

    z__[j + j * z_dim1] = 1.;


/* L80: */
  }

  kl = *igh - *low - 1;
  if(kl < 1) {
    goto L200;
  }


/*     .......... for mp=igh-1 step -1 until low+1 do -- .......... */
  i__1 = kl;
  for(mm = 1; mm <= i__1; ++mm) {
    mp = *igh - mm;
    mp1 = mp + 1;

    i__2 = *igh;
    for(i__ = mp1; i__ <= i__2; ++i__) {


/* L100: */
      z__[i__ + mp * z_dim1] = a[i__ + (mp - 1) * a_dim1];
    }

    i__ = int__[mp];
    if(i__ == mp) {
      goto L140;
    }

    i__2 = *igh;
    for(j = mp; j <= i__2; ++j) {
      z__[mp + j * z_dim1] = z__[i__ + j * z_dim1];
      z__[i__ + j * z_dim1] = 0.;


/* L130: */
    }

    z__[i__ + mp * z_dim1] = 1.;
  L140:
    ;
  }

L200:
  return 0;
}                               /* eltran_ */

static int hqr_(integer * nm, integer * n, integer * low, integer * igh,
                doublereal * h__, doublereal * wr, doublereal * wi, integer * ierr)
{
  /* System generated locals */
  integer h_dim1, h_offset, i__1, i__2, i__3;
  doublereal d__1, d__2;

  /* Local variables */
  doublereal norm;
  integer i__, j, k, l = 0, m = 0;
  doublereal p = 0.0, q = 0.0, r__ = 0.0, s, t, w, x, y;
  integer na, en, ll, mm;
  doublereal zz;
  logical notlas;
  integer mp2, itn, its, enm2;
  doublereal tst1, tst2;


/*  RESTORED CORRECT INDICES OF LOOPS (200,210,230,240). (9/29/89 BSG) */


/*     this subroutine is a translation of the algol procedure hqr, */


/*     num. math. 14, 219-231(1970) by martin, peters, and wilkinson. */


/*     handbook for auto. comp., vol.ii-linear algebra, 359-371(1971). */


/*     this subroutine finds the eigenvalues of a real */


/*     upper hessenberg matrix by the qr method. */


/*     on input */


/*        nm must be set to the row dimension of two-dimensional */


/*          array parameters as declared in the calling program */


/*          dimension statement. */


/*        n is the order of the matrix. */


/*        low and igh are integers determined by the balancing */


/*          subroutine  balanc.  if  balanc  has not been used, */


/*          set low=1, igh=n. */


/*        h contains the upper hessenberg matrix.  information about */


/*          the transformations used in the reduction to hessenberg */


/*          form by  elmhes  or  orthes, if performed, is stored */


/*          in the remaining triangle under the hessenberg matrix. */


/*     on output */


/*        h has been destroyed.  therefore, it must be saved */


/*          before calling  hqr  if subsequent calculation and */


/*          back transformation of eigenvectors is to be performed. */


/*        wr and wi contain the real and imaginary parts, */


/*          respectively, of the eigenvalues.  the eigenvalues */


/*          are unordered except that complex conjugate pairs */


/*          of values appear consecutively with the eigenvalue */


/*          having the positive imaginary part first.  if an */


/*          error exit is made, the eigenvalues should be correct */


/*          for indices ierr+1,...,n. */


/*        ierr is set to */


/*          zero       for normal return, */


/*          j          if the limit of 30*n iterations is exhausted */


/*                     while the j-th eigenvalue is being sought. */


/*     questions and comments should be directed to burton s. garbow, */


/*     mathematics and computer science div, argonne national laboratory 
*/


/*     this version dated september 1989. */


/*     ------------------------------------------------------------------ 
*/

  /* Parameter adjustments */
  --wi;
  --wr;
  h_dim1 = *nm;
  h_offset = h_dim1 + 1;
  h__ -= h_offset;

  /* Function Body */
  *ierr = 0;
  norm = 0.;
  k = 1;


/*     .......... store roots isolated by balanc */


/*                and compute matrix norm .......... */
  i__1 = *n;
  for(i__ = 1; i__ <= i__1; ++i__) {

    i__2 = *n;
    for(j = k; j <= i__2; ++j) {


/* L40: */
      norm += (d__1 = h__[i__ + j * h_dim1], abs(d__1));
    }

    k = i__;
    if(i__ >= *low && i__ <= *igh) {
      goto L50;
    }
    wr[i__] = h__[i__ + i__ * h_dim1];
    wi[i__] = 0.;
  L50:
    ;
  }

  en = *igh;
  t = 0.;
  itn = *n * 30;


/*     .......... search for next eigenvalues .......... */
L60:
  if(en < *low) {
    goto L1001;
  }
  its = 0;
  na = en - 1;
  enm2 = na - 1;


/*     .......... look for single small sub-diagonal element */


/*                for l=en step -1 until low do -- .......... */
L70:
  i__1 = en;
  for(ll = *low; ll <= i__1; ++ll) {
    l = en + *low - ll;
    if(l == *low) {
      goto L100;
    }
    s = (d__1 = h__[l - 1 + (l - 1) * h_dim1], abs(d__1)) + (d__2 = h__[l
                                                                        + l * h_dim1],
                                                             abs(d__2));
    if(s == 0.) {
      s = norm;
    }
    tst1 = s;
    tst2 = tst1 + (d__1 = h__[l + (l - 1) * h_dim1], abs(d__1));
    if(tst2 == tst1) {
      goto L100;
    }


/* L80: */
  }


/*     .......... form shift .......... */
L100:
  x = h__[en + en * h_dim1];
  if(l == en) {
    goto L270;
  }
  y = h__[na + na * h_dim1];
  w = h__[en + na * h_dim1] * h__[na + en * h_dim1];
  if(l == na) {
    goto L280;
  }
  if(itn == 0) {
    goto L1000;
  }
  if(its != 10 && its != 20) {
    goto L130;
  }


/*     .......... form exceptional shift .......... */
  t += x;

  i__1 = en;
  for(i__ = *low; i__ <= i__1; ++i__) {


/* L120: */
    h__[i__ + i__ * h_dim1] -= x;
  }

  s = (d__1 = h__[en + na * h_dim1], abs(d__1)) + (d__2 = h__[na + enm2 *
                                                              h_dim1], abs(d__2));
  x = s * .75;
  y = x;
  w = s * -.4375 * s;
L130:
  ++its;
  --itn;


/*     .......... look for two consecutive small */


/*                sub-diagonal elements. */


/*                for m=en-2 step -1 until l do -- .......... */
  i__1 = enm2;
  for(mm = l; mm <= i__1; ++mm) {
    m = enm2 + l - mm;
    zz = h__[m + m * h_dim1];
    r__ = x - zz;
    s = y - zz;
    p = (r__ * s - w) / h__[m + 1 + m * h_dim1] + h__[m + (m + 1) * h_dim1];
    q = h__[m + 1 + (m + 1) * h_dim1] - zz - r__ - s;
    r__ = h__[m + 2 + (m + 1) * h_dim1];
    s = abs(p) + abs(q) + abs(r__);
    p /= s;
    q /= s;
    r__ /= s;
    if(m == l) {
      goto L150;
    }
    tst1 = abs(p) * ((d__1 = h__[m - 1 + (m - 1) * h_dim1], abs(d__1)) +
                     abs(zz) + (d__2 = h__[m + 1 + (m + 1) * h_dim1], abs(d__2)));
    tst2 = tst1 + (d__1 = h__[m + (m - 1) * h_dim1], abs(d__1)) * (abs(q)
                                                                   + abs(r__));
    if(tst2 == tst1) {
      goto L150;
    }


/* L140: */
  }

L150:
  mp2 = m + 2;

  i__1 = en;
  for(i__ = mp2; i__ <= i__1; ++i__) {
    h__[i__ + (i__ - 2) * h_dim1] = 0.;
    if(i__ == mp2) {
      goto L160;
    }
    h__[i__ + (i__ - 3) * h_dim1] = 0.;
  L160:
    ;
  }


/*     .......... double qr step involving rows l to en and */


/*                columns m to en .......... */
  i__1 = na;
  for(k = m; k <= i__1; ++k) {
    notlas = k != na;
    if(k == m) {
      goto L170;
    }
    p = h__[k + (k - 1) * h_dim1];
    q = h__[k + 1 + (k - 1) * h_dim1];
    r__ = 0.;
    if(notlas) {
      r__ = h__[k + 2 + (k - 1) * h_dim1];
    }
    x = abs(p) + abs(q) + abs(r__);
    if(x == 0.) {
      goto L260;
    }
    p /= x;
    q /= x;
    r__ /= x;
  L170:
    d__1 = sqrt1d(p * p + q * q + r__ * r__);
    s = d_sign(&d__1, &p);
    if(k == m) {
      goto L180;
    }
    h__[k + (k - 1) * h_dim1] = -s * x;
    goto L190;
  L180:
    if(l != m) {
      h__[k + (k - 1) * h_dim1] = -h__[k + (k - 1) * h_dim1];
    }
  L190:
    p += s;
    x = p / s;
    y = q / s;
    zz = r__ / s;
    q /= p;
    r__ /= p;
    if(notlas) {
      goto L225;
    }


/*     .......... row modification .......... */
    i__2 = en;
    for(j = k; j <= i__2; ++j) {
      p = h__[k + j * h_dim1] + q * h__[k + 1 + j * h_dim1];
      h__[k + j * h_dim1] -= p * x;
      h__[k + 1 + j * h_dim1] -= p * y;


/* L200: */
    }


/* Computing MIN */
    i__2 = en, i__3 = k + 3;
    j = mymin(i__2, i__3);


/*     .......... column modification .......... */
    i__2 = j;
    for(i__ = l; i__ <= i__2; ++i__) {
      p = x * h__[i__ + k * h_dim1] + y * h__[i__ + (k + 1) * h_dim1];
      h__[i__ + k * h_dim1] -= p;
      h__[i__ + (k + 1) * h_dim1] -= p * q;


/* L210: */
    }
    goto L255;
  L225:


/*     .......... row modification .......... */
    i__2 = en;
    for(j = k; j <= i__2; ++j) {
      p =
        h__[k + j * h_dim1] + q * h__[k + 1 + j * h_dim1] + r__ * h__[k + 2 + j * h_dim1];
      h__[k + j * h_dim1] -= p * x;
      h__[k + 1 + j * h_dim1] -= p * y;
      h__[k + 2 + j * h_dim1] -= p * zz;


/* L230: */
    }


/* Computing MIN */
    i__2 = en, i__3 = k + 3;
    j = mymin(i__2, i__3);


/*     .......... column modification .......... */
    i__2 = j;
    for(i__ = l; i__ <= i__2; ++i__) {
      p = x * h__[i__ + k * h_dim1] + y * h__[i__ + (k + 1) * h_dim1] +
        zz * h__[i__ + (k + 2) * h_dim1];
      h__[i__ + k * h_dim1] -= p;
      h__[i__ + (k + 1) * h_dim1] -= p * q;
      h__[i__ + (k + 2) * h_dim1] -= p * r__;


/* L240: */
    }
  L255:

  L260:
    ;
  }

  goto L70;


/*     .......... one root found .......... */
L270:
  wr[en] = x + t;
  wi[en] = 0.;
  en = na;
  goto L60;


/*     .......... two roots found .......... */
L280:
  p = (y - x) / 2.;
  q = p * p + w;
  zz = sqrt1d((abs(q)));
  x += t;
  if(q < 0.) {
    goto L320;
  }


/*     .......... real pair .......... */
  zz = p + d_sign(&zz, &p);
  wr[na] = x + zz;
  wr[en] = wr[na];
  if(zz != 0.) {
    wr[en] = x - w / zz;
  }
  wi[na] = 0.;
  wi[en] = 0.;
  goto L330;


/*     .......... complex pair .......... */
L320:
  wr[na] = x + p;
  wr[en] = x + p;
  wi[na] = zz;
  wi[en] = -zz;
L330:
  en = enm2;
  goto L60;


/*     .......... set error -- all eigenvalues have not */


/*                converged after 30*n iterations .......... */
L1000:
  *ierr = en;
L1001:
  return 0;
}                               /* hqr_ */

static int hqr2_(integer * nm, integer * n, integer * low, integer * igh,
                 doublereal * h__, doublereal * wr, doublereal * wi, doublereal * z__,
                 integer * ierr)
{
  /* System generated locals */
  integer h_dim1, h_offset, z_dim1, z_offset, i__1, i__2, i__3;
  doublereal d__1, d__2, d__3, d__4;

  /* Local variables */
  doublereal norm;
  integer i__, j, k, l = 0, m = 0;
  doublereal p = 0.0, q = 0.0, r__ = 0.0, s = 0.0, t, w, x, y;
  integer na, ii, en, jj;
  doublereal ra, sa;
  integer ll, mm, nn;
  doublereal vi, vr, zz = 0.0;
  logical notlas;
  integer mp2, itn, its, enm2;
  doublereal tst1, tst2;


/*     this subroutine is a translation of the algol procedure hqr2, */


/*     num. math. 16, 181-204(1970) by peters and wilkinson. */


/*     handbook for auto. comp., vol.ii-linear algebra, 372-395(1971). */


/*     this subroutine finds the eigenvalues and eigenvectors */


/*     of a real upper hessenberg matrix by the qr method.  the */


/*     eigenvectors of a real general matrix can also be found */


/*     if  elmhes  and  eltran  or  orthes  and  ortran  have */


/*     been used to reduce this general matrix to hessenberg form */


/*     and to accumulate the similarity transformations. */


/*     on input */


/*        nm must be set to the row dimension of two-dimensional */


/*          array parameters as declared in the calling program */


/*          dimension statement. */


/*        n is the order of the matrix. */


/*        low and igh are integers determined by the balancing */


/*          subroutine  balanc.  if  balanc  has not been used, */


/*          set low=1, igh=n. */


/*        h contains the upper hessenberg matrix. */


/*        z contains the transformation matrix produced by  eltran */


/*          after the reduction by  elmhes, or by  ortran  after the */


/*          reduction by  orthes, if performed.  if the eigenvectors */


/*          of the hessenberg matrix are desired, z must contain the */


/*          identity matrix. */


/*     on output */


/*        h has been destroyed. */


/*        wr and wi contain the real and imaginary parts, */


/*          respectively, of the eigenvalues.  the eigenvalues */


/*          are unordered except that complex conjugate pairs */


/*          of values appear consecutively with the eigenvalue */


/*          having the positive imaginary part first.  if an */


/*          error exit is made, the eigenvalues should be correct */


/*          for indices ierr+1,...,n. */


/*        z contains the real and imaginary parts of the eigenvectors. */


/*          if the i-th eigenvalue is real, the i-th column of z */


/*          contains its eigenvector.  if the i-th eigenvalue is complex 
*/


/*          with positive imaginary part, the i-th and (i+1)-th */


/*          columns of z contain the real and imaginary parts of its */


/*          eigenvector.  the eigenvectors are unnormalized.  if an */


/*          error exit is made, none of the eigenvectors has been found. 
*/


/*        ierr is set to */


/*          zero       for normal return, */


/*          j          if the limit of 30*n iterations is exhausted */


/*                     while the j-th eigenvalue is being sought. */


/*     calls cdiv for complex division. */


/*     questions and comments should be directed to burton s. garbow, */


/*     mathematics and computer science div, argonne national laboratory 
*/


/*     this version dated august 1983. */


/*     ------------------------------------------------------------------ 
*/

  /* Parameter adjustments */
  z_dim1 = *nm;
  z_offset = z_dim1 + 1;
  z__ -= z_offset;
  --wi;
  --wr;
  h_dim1 = *nm;
  h_offset = h_dim1 + 1;
  h__ -= h_offset;

  /* Function Body */
  *ierr = 0;
  norm = 0.;
  k = 1;


/*     .......... store roots isolated by balanc */


/*                and compute matrix norm .......... */
  i__1 = *n;
  for(i__ = 1; i__ <= i__1; ++i__) {

    i__2 = *n;
    for(j = k; j <= i__2; ++j) {


/* L40: */
      norm += (d__1 = h__[i__ + j * h_dim1], abs(d__1));
    }

    k = i__;
    if(i__ >= *low && i__ <= *igh) {
      goto L50;
    }
    wr[i__] = h__[i__ + i__ * h_dim1];
    wi[i__] = 0.;
  L50:
    ;
  }

  en = *igh;
  t = 0.;
  itn = *n * 30;


/*     .......... search for next eigenvalues .......... */
L60:
  if(en < *low) {
    goto L340;
  }
  its = 0;
  na = en - 1;
  enm2 = na - 1;


/*     .......... look for single small sub-diagonal element */


/*                for l=en step -1 until low do -- .......... */
L70:
  i__1 = en;
  for(ll = *low; ll <= i__1; ++ll) {
    l = en + *low - ll;
    if(l == *low) {
      goto L100;
    }
    s = (d__1 = h__[l - 1 + (l - 1) * h_dim1], abs(d__1)) + (d__2 = h__[l
                                                                        + l * h_dim1],
                                                             abs(d__2));
    if(s == 0.) {
      s = norm;
    }
    tst1 = s;
    tst2 = tst1 + (d__1 = h__[l + (l - 1) * h_dim1], abs(d__1));
    if(tst2 == tst1) {
      goto L100;
    }


/* L80: */
  }


/*     .......... form shift .......... */
L100:
  x = h__[en + en * h_dim1];
  if(l == en) {
    goto L270;
  }
  y = h__[na + na * h_dim1];
  w = h__[en + na * h_dim1] * h__[na + en * h_dim1];
  if(l == na) {
    goto L280;
  }
  if(itn == 0) {
    goto L1000;
  }
  if(its != 10 && its != 20) {
    goto L130;
  }


/*     .......... form exceptional shift .......... */
  t += x;

  i__1 = en;
  for(i__ = *low; i__ <= i__1; ++i__) {


/* L120: */
    h__[i__ + i__ * h_dim1] -= x;
  }

  s = (d__1 = h__[en + na * h_dim1], abs(d__1)) + (d__2 = h__[na + enm2 *
                                                              h_dim1], abs(d__2));
  x = s * .75;
  y = x;
  w = s * -.4375 * s;
L130:
  ++its;
  --itn;


/*     .......... look for two consecutive small */


/*                sub-diagonal elements. */


/*                for m=en-2 step -1 until l do -- .......... */
  i__1 = enm2;
  for(mm = l; mm <= i__1; ++mm) {
    m = enm2 + l - mm;
    zz = h__[m + m * h_dim1];
    r__ = x - zz;
    s = y - zz;
    p = (r__ * s - w) / h__[m + 1 + m * h_dim1] + h__[m + (m + 1) * h_dim1];
    q = h__[m + 1 + (m + 1) * h_dim1] - zz - r__ - s;
    r__ = h__[m + 2 + (m + 1) * h_dim1];
    s = abs(p) + abs(q) + abs(r__);
    p /= s;
    q /= s;
    r__ /= s;
    if(m == l) {
      goto L150;
    }
    tst1 = abs(p) * ((d__1 = h__[m - 1 + (m - 1) * h_dim1], abs(d__1)) +
                     abs(zz) + (d__2 = h__[m + 1 + (m + 1) * h_dim1], abs(d__2)));
    tst2 = tst1 + (d__1 = h__[m + (m - 1) * h_dim1], abs(d__1)) * (abs(q)
                                                                   + abs(r__));
    if(tst2 == tst1) {
      goto L150;
    }


/* L140: */
  }

L150:
  mp2 = m + 2;

  i__1 = en;
  for(i__ = mp2; i__ <= i__1; ++i__) {
    h__[i__ + (i__ - 2) * h_dim1] = 0.;
    if(i__ == mp2) {
      goto L160;
    }
    h__[i__ + (i__ - 3) * h_dim1] = 0.;
  L160:
    ;
  }


/*     .......... double qr step involving rows l to en and */


/*                columns m to en .......... */
  i__1 = na;
  for(k = m; k <= i__1; ++k) {
    notlas = k != na;
    if(k == m) {
      goto L170;
    }
    p = h__[k + (k - 1) * h_dim1];
    q = h__[k + 1 + (k - 1) * h_dim1];
    r__ = 0.;
    if(notlas) {
      r__ = h__[k + 2 + (k - 1) * h_dim1];
    }
    x = abs(p) + abs(q) + abs(r__);
    if(x == 0.) {
      goto L260;
    }
    p /= x;
    q /= x;
    r__ /= x;
  L170:
    d__1 = sqrt1d(p * p + q * q + r__ * r__);
    s = d_sign(&d__1, &p);
    if(k == m) {
      goto L180;
    }
    h__[k + (k - 1) * h_dim1] = -s * x;
    goto L190;
  L180:
    if(l != m) {
      h__[k + (k - 1) * h_dim1] = -h__[k + (k - 1) * h_dim1];
    }
  L190:
    p += s;
    x = p / s;
    y = q / s;
    zz = r__ / s;
    q /= p;
    r__ /= p;
    if(notlas) {
      goto L225;
    }


/*     .......... row modification .......... */
    i__2 = *n;
    for(j = k; j <= i__2; ++j) {
      p = h__[k + j * h_dim1] + q * h__[k + 1 + j * h_dim1];
      h__[k + j * h_dim1] -= p * x;
      h__[k + 1 + j * h_dim1] -= p * y;


/* L200: */
    }


/* Computing MIN */
    i__2 = en, i__3 = k + 3;
    j = mymin(i__2, i__3);


/*     .......... column modification .......... */
    i__2 = j;
    for(i__ = 1; i__ <= i__2; ++i__) {
      p = x * h__[i__ + k * h_dim1] + y * h__[i__ + (k + 1) * h_dim1];
      h__[i__ + k * h_dim1] -= p;
      h__[i__ + (k + 1) * h_dim1] -= p * q;


/* L210: */
    }


/*     .......... accumulate transformations .......... */
    i__2 = *igh;
    for(i__ = *low; i__ <= i__2; ++i__) {
      p = x * z__[i__ + k * z_dim1] + y * z__[i__ + (k + 1) * z_dim1];
      z__[i__ + k * z_dim1] -= p;
      z__[i__ + (k + 1) * z_dim1] -= p * q;


/* L220: */
    }
    goto L255;
  L225:


/*     .......... row modification .......... */
    i__2 = *n;
    for(j = k; j <= i__2; ++j) {
      p =
        h__[k + j * h_dim1] + q * h__[k + 1 + j * h_dim1] + r__ * h__[k + 2 + j * h_dim1];
      h__[k + j * h_dim1] -= p * x;
      h__[k + 1 + j * h_dim1] -= p * y;
      h__[k + 2 + j * h_dim1] -= p * zz;


/* L230: */
    }


/* Computing MIN */
    i__2 = en, i__3 = k + 3;
    j = mymin(i__2, i__3);


/*     .......... column modification .......... */
    i__2 = j;
    for(i__ = 1; i__ <= i__2; ++i__) {
      p = x * h__[i__ + k * h_dim1] + y * h__[i__ + (k + 1) * h_dim1] +
        zz * h__[i__ + (k + 2) * h_dim1];
      h__[i__ + k * h_dim1] -= p;
      h__[i__ + (k + 1) * h_dim1] -= p * q;
      h__[i__ + (k + 2) * h_dim1] -= p * r__;


/* L240: */
    }


/*     .......... accumulate transformations .......... */
    i__2 = *igh;
    for(i__ = *low; i__ <= i__2; ++i__) {
      p = x * z__[i__ + k * z_dim1] + y * z__[i__ + (k + 1) * z_dim1] +
        zz * z__[i__ + (k + 2) * z_dim1];
      z__[i__ + k * z_dim1] -= p;
      z__[i__ + (k + 1) * z_dim1] -= p * q;
      z__[i__ + (k + 2) * z_dim1] -= p * r__;


/* L250: */
    }
  L255:

  L260:
    ;
  }

  goto L70;


/*     .......... one root found .......... */
L270:
  h__[en + en * h_dim1] = x + t;
  wr[en] = h__[en + en * h_dim1];
  wi[en] = 0.;
  en = na;
  goto L60;


/*     .......... two roots found .......... */
L280:
  p = (y - x) / 2.;
  q = p * p + w;
  zz = sqrt1d((abs(q)));
  h__[en + en * h_dim1] = x + t;
  x = h__[en + en * h_dim1];
  h__[na + na * h_dim1] = y + t;
  if(q < 0.) {
    goto L320;
  }


/*     .......... real pair .......... */
  zz = p + d_sign(&zz, &p);
  wr[na] = x + zz;
  wr[en] = wr[na];
  if(zz != 0.) {
    wr[en] = x - w / zz;
  }
  wi[na] = 0.;
  wi[en] = 0.;
  x = h__[en + na * h_dim1];
  s = abs(x) + abs(zz);
  p = x / s;
  q = zz / s;
  r__ = sqrt1d(p * p + q * q);
  p /= r__;
  q /= r__;


/*     .......... row modification .......... */
  i__1 = *n;
  for(j = na; j <= i__1; ++j) {
    zz = h__[na + j * h_dim1];
    h__[na + j * h_dim1] = q * zz + p * h__[en + j * h_dim1];
    h__[en + j * h_dim1] = q * h__[en + j * h_dim1] - p * zz;


/* L290: */
  }


/*     .......... column modification .......... */
  i__1 = en;
  for(i__ = 1; i__ <= i__1; ++i__) {
    zz = h__[i__ + na * h_dim1];
    h__[i__ + na * h_dim1] = q * zz + p * h__[i__ + en * h_dim1];
    h__[i__ + en * h_dim1] = q * h__[i__ + en * h_dim1] - p * zz;


/* L300: */
  }


/*     .......... accumulate transformations .......... */
  i__1 = *igh;
  for(i__ = *low; i__ <= i__1; ++i__) {
    zz = z__[i__ + na * z_dim1];
    z__[i__ + na * z_dim1] = q * zz + p * z__[i__ + en * z_dim1];
    z__[i__ + en * z_dim1] = q * z__[i__ + en * z_dim1] - p * zz;


/* L310: */
  }

  goto L330;


/*     .......... complex pair .......... */
L320:
  wr[na] = x + p;
  wr[en] = x + p;
  wi[na] = zz;
  wi[en] = -zz;
L330:
  en = enm2;
  goto L60;


/*     .......... all roots found.  backsubstitute to find */


/*                vectors of upper triangular form .......... */
L340:
  if(norm == 0.) {
    goto L1001;
  }


/*     .......... for en=n step -1 until 1 do -- .......... */
  i__1 = *n;
  for(nn = 1; nn <= i__1; ++nn) {
    en = *n + 1 - nn;
    p = wr[en];
    q = wi[en];
    na = en - 1;
    if(q < 0.) {
      goto L710;
    } else if(q == 0) {
      goto L600;
    } else {
      goto L800;
    }


/*     .......... real vector .......... */
  L600:
    m = en;
    h__[en + en * h_dim1] = 1.;
    if(na == 0) {
      goto L800;
    }


/*     .......... for i=en-1 step -1 until 1 do -- .......... */
    i__2 = na;
    for(ii = 1; ii <= i__2; ++ii) {
      i__ = en - ii;
      w = h__[i__ + i__ * h_dim1] - p;
      r__ = 0.;

      i__3 = en;
      for(j = m; j <= i__3; ++j) {


/* L610: */
        r__ += h__[i__ + j * h_dim1] * h__[j + en * h_dim1];
      }

      if(wi[i__] >= 0.) {
        goto L630;
      }
      zz = w;
      s = r__;
      goto L700;
    L630:
      m = i__;
      if(wi[i__] != 0.) {
        goto L640;
      }
      t = w;
      if(t != 0.) {
        goto L635;
      }
      tst1 = norm;
      t = tst1;
    L632:
      t *= .01;
      tst2 = norm + t;
      if(tst2 > tst1) {
        goto L632;
      }
    L635:
      h__[i__ + en * h_dim1] = -r__ / t;
      goto L680;


/*     .......... solve real equations .......... */
    L640:
      x = h__[i__ + (i__ + 1) * h_dim1];
      y = h__[i__ + 1 + i__ * h_dim1];
      q = (wr[i__] - p) * (wr[i__] - p) + wi[i__] * wi[i__];
      t = (x * s - zz * r__) / q;
      h__[i__ + en * h_dim1] = t;
      if(abs(x) <= abs(zz)) {
        goto L650;
      }
      h__[i__ + 1 + en * h_dim1] = (-r__ - w * t) / x;
      goto L680;
    L650:
      h__[i__ + 1 + en * h_dim1] = (-s - y * t) / zz;


/*     .......... overflow control .......... */
    L680:
      t = (d__1 = h__[i__ + en * h_dim1], abs(d__1));
      if(t == 0.) {
        goto L700;
      }
      tst1 = t;
      tst2 = tst1 + 1. / tst1;
      if(tst2 > tst1) {
        goto L700;
      }
      i__3 = en;
      for(j = i__; j <= i__3; ++j) {
        h__[j + en * h_dim1] /= t;


/* L690: */
      }

    L700:
      ;
    }


/*     .......... end real vector .......... */
    goto L800;


/*     .......... complex vector .......... */
  L710:
    m = na;


/*     .......... last vector component chosen imaginary so that */


/*                eigenvector matrix is triangular .......... */
    if((d__1 = h__[en + na * h_dim1], abs(d__1)) <= (d__2 = h__[na + en *
                                                                h_dim1], abs(d__2))) {
      goto L720;
    }
    h__[na + na * h_dim1] = q / h__[en + na * h_dim1];
    h__[na + en * h_dim1] = -(h__[en + en * h_dim1] - p) / h__[en + na * h_dim1];
    goto L730;
  L720:
    d__1 = -h__[na + en * h_dim1];
    d__2 = h__[na + na * h_dim1] - p;
    cdiv_(&c_b126, &d__1, &d__2, &q, &h__[na + na * h_dim1], &h__[na + en * h_dim1]);
  L730:
    h__[en + na * h_dim1] = 0.;
    h__[en + en * h_dim1] = 1.;
    enm2 = na - 1;
    if(enm2 == 0) {
      goto L800;
    }


/*     .......... for i=en-2 step -1 until 1 do -- .......... */
    i__2 = enm2;
    for(ii = 1; ii <= i__2; ++ii) {
      i__ = na - ii;
      w = h__[i__ + i__ * h_dim1] - p;
      ra = 0.;
      sa = 0.;

      i__3 = en;
      for(j = m; j <= i__3; ++j) {
        ra += h__[i__ + j * h_dim1] * h__[j + na * h_dim1];
        sa += h__[i__ + j * h_dim1] * h__[j + en * h_dim1];


/* L760: */
      }

      if(wi[i__] >= 0.) {
        goto L770;
      }
      zz = w;
      r__ = ra;
      s = sa;
      goto L795;
    L770:
      m = i__;
      if(wi[i__] != 0.) {
        goto L780;
      }
      d__1 = -ra;
      d__2 = -sa;
      cdiv_(&d__1, &d__2, &w, &q, &h__[i__ + na * h_dim1], &h__[i__ + en * h_dim1]);
      goto L790;


/*     .......... solve complex equations .......... */
    L780:
      x = h__[i__ + (i__ + 1) * h_dim1];
      y = h__[i__ + 1 + i__ * h_dim1];
      vr = (wr[i__] - p) * (wr[i__] - p) + wi[i__] * wi[i__] - q * q;
      vi = (wr[i__] - p) * 2. * q;
      if(vr != 0. || vi != 0.) {
        goto L784;
      }
      tst1 = norm * (abs(w) + abs(q) + abs(x) + abs(y) + abs(zz));
      vr = tst1;
    L783:
      vr *= .01;
      tst2 = tst1 + vr;
      if(tst2 > tst1) {
        goto L783;
      }
    L784:
      d__1 = x * r__ - zz * ra + q * sa;
      d__2 = x * s - zz * sa - q * ra;
      cdiv_(&d__1, &d__2, &vr, &vi, &h__[i__ + na * h_dim1], &h__[i__ + en * h_dim1]);
      if(abs(x) <= abs(zz) + abs(q)) {
        goto L785;
      }
      h__[i__ + 1 + na * h_dim1] = (-ra - w * h__[i__ + na * h_dim1] +
                                    q * h__[i__ + en * h_dim1]) / x;
      h__[i__ + 1 + en * h_dim1] = (-sa - w * h__[i__ + en * h_dim1] -
                                    q * h__[i__ + na * h_dim1]) / x;
      goto L790;
    L785:
      d__1 = -r__ - y * h__[i__ + na * h_dim1];
      d__2 = -s - y * h__[i__ + en * h_dim1];
      cdiv_(&d__1, &d__2, &zz, &q, &h__[i__ + 1 + na * h_dim1],
            &h__[i__ + 1 + en * h_dim1]);


/*     .......... overflow control .......... */
    L790:


/* Computing MAX */
      d__3 = (d__1 = h__[i__ + na * h_dim1], abs(d__1)), d__4 = (d__2 =
                                                                 h__[i__ + en * h_dim1],
                                                                 abs(d__2));
      t = mymax(d__3, d__4);
      if(t == 0.) {
        goto L795;
      }
      tst1 = t;
      tst2 = tst1 + 1. / tst1;
      if(tst2 > tst1) {
        goto L795;
      }
      i__3 = en;
      for(j = i__; j <= i__3; ++j) {
        h__[j + na * h_dim1] /= t;
        h__[j + en * h_dim1] /= t;


/* L792: */
      }

    L795:
      ;
    }


/*     .......... end complex vector .......... */
  L800:
    ;
  }


/*     .......... end back substitution. */


/*                vectors of isolated roots .......... */
  i__1 = *n;
  for(i__ = 1; i__ <= i__1; ++i__) {
    if(i__ >= *low && i__ <= *igh) {
      goto L840;
    }

    i__2 = *n;
    for(j = i__; j <= i__2; ++j) {


/* L820: */
      z__[i__ + j * z_dim1] = h__[i__ + j * h_dim1];
    }

  L840:
    ;
  }


/*     .......... multiply by transformation matrix to give */


/*                vectors of original full matrix. */


/*                for j=n step -1 until low do -- .......... */
  i__1 = *n;
  for(jj = *low; jj <= i__1; ++jj) {
    j = *n + *low - jj;
    m = mymin(j, *igh);

    i__2 = *igh;
    for(i__ = *low; i__ <= i__2; ++i__) {
      zz = 0.;

      i__3 = m;
      for(k = *low; k <= i__3; ++k) {


/* L860: */
        zz += z__[i__ + k * z_dim1] * h__[k + j * h_dim1];
      }

      z__[i__ + j * z_dim1] = zz;


/* L880: */
    }
  }

  goto L1001;


/*     .......... set error -- all eigenvalues have not */


/*                converged after 30*n iterations .......... */
L1000:
  *ierr = en;
L1001:
  return 0;
}                               /* hqr2_ */

int pymol_rg_(integer * nm, integer * n, doublereal * a, doublereal * wr,
              doublereal * wi, integer * matz, doublereal * z__, integer * iv1,
              doublereal * fv1, integer * ierr)
{
  /* System generated locals */
  integer a_dim1, a_offset, z_dim1, z_offset;

  /* Local variables */
  integer is1, is2;


/*     this subroutine calls the recommended sequence of */


/*     subroutines from the eigensystem subroutine package (eispack) */


/*     to find the eigenvalues and eigenvectors (if desired) */


/*     of a real general matrix. */


/*     on input */


/*        nm  must be set to the row dimension of the two-dimensional */


/*        array parameters as declared in the calling program */


/*        dimension statement. */


/*        n  is the order of the matrix  a. */


/*        a  contains the real general matrix. */


/*        matz  is an integer variable set equal to zero if */


/*        only eigenvalues are desired.  otherwise it is set to */


/*        any non-zero integer for both eigenvalues and eigenvectors. */


/*     on output */


/*        wr  and  wi  contain the real and imaginary parts, */


/*        respectively, of the eigenvalues.  complex conjugate */


/*        pairs of eigenvalues appear consecutively with the */


/*        eigenvalue having the positive imaginary part first. */


/*        z  contains the real and imaginary parts of the eigenvectors */


/*        if matz is not zero.  if the j-th eigenvalue is real, the */


/*        j-th column of  z  contains its eigenvector.  if the j-th */


/*        eigenvalue is complex with positive imaginary part, the */


/*        j-th and (j+1)-th columns of  z  contain the real and */


/*        imaginary parts of its eigenvector.  the conjugate of this */


/*        vector is the eigenvector for the conjugate eigenvalue. */


/*        ierr  is an integer output variable set equal to an error */


/*           completion code described in the documentation for hqr */


/*           and hqr2.  the normal completion code is zero. */


/*        iv1  and  fv1  are temporary storage arrays. */


/*     questions and comments should be directed to burton s. garbow, */


/*     mathematics and computer science div, argonne national laboratory 
*/


/*     this version dated august 1983. */


/*     ------------------------------------------------------------------ 
*/

  /* Parameter adjustments */
  --fv1;
  --iv1;
  z_dim1 = *nm;
  z_offset = z_dim1 + 1;
  z__ -= z_offset;
  --wi;
  --wr;
  a_dim1 = *nm;
  a_offset = a_dim1 + 1;
  a -= a_offset;

  /* Function Body */
  if(*n <= *nm) {
    goto L10;
  }
  *ierr = *n * 10;
  goto L50;

L10:
  balanc_(nm, n, &a[a_offset], &is1, &is2, &fv1[1]);
  elmhes_(nm, n, &is1, &is2, &a[a_offset], &iv1[1]);
  if(*matz != 0) {
    goto L20;
  }


/*     .......... find eigenvalues only .......... */
  hqr_(nm, n, &is1, &is2, &a[a_offset], &wr[1], &wi[1], ierr);
  goto L50;


/*     .......... find both eigenvalues and eigenvectors .......... */
L20:
  eltran_(nm, n, &is1, &is2, &a[a_offset], &iv1[1], &z__[z_offset]);
  hqr2_(nm, n, &is1, &is2, &a[a_offset], &wr[1], &wi[1], &z__[z_offset], ierr);
  if(*ierr != 0) {
    goto L50;
  }
  balbak_(nm, n, &is1, &is2, &fv1[1], n, &z__[z_offset]);
L50:
  return 0;
}                               /* rg_ */
